Search

Let (N, g) be a Riemannian manifold, by using the musical isomorphisms ... and ... induced by g, we built a bridge between the geometry of the tangent bundle TN (resp. the unit tangent sphere bundle T1N) equipped with the Sasaki metric gS (resp. the induced Sasaki metric ḡS) and that of the cotangent bundle T*N (resp. the unit cotangent sphere bundle T1* endowed with the Sasaki metric gS (resp. the induced Sasaki metric GS). Moreover, we prove that T1*N carries a contact metric structure and study some of its properties. [ABSTRACT FROM AUTHOR]

Given an open neighborhood 풲 of the zero section in the cotangent bundle of N we define a distance-like function ρ풲 on N using certain symplectic embeddings from the standard ball B2n(r) to 풲. We show that when 풲 is the unit-disk cotangent bundle of a Riemannian metric on N, ρ풲 recovers the metric. As an intermediate step, we give a new construction of a symplectic embedding of the ball of capacity 4 to the product of Lagrangian disks PL := Bn(1) × Bn(1), and we give a new proof of the strong Viterbo conjecture about normalized capacities for PL. We also give bounds of the symplectic packing number of two balls in a unit-disk cotangent bundle relative to the zero section N. [ABSTRACT FROM AUTHOR]

In this paper we show some Lefschetz-type theorems for the effective cone of Hyperkähler varieties. In particular we are able to show that the inclusion of any smooth ample divisor induces an isomorphism of effective cones. Moreover we deduce a similar statement for some effective exceptional divisors, which yields the computation of the effective cone of e.g. projectivized cotangent bundles or some projectivized Lazarsfeld–Mukai bundles. [ABSTRACT FROM AUTHOR]

Let (M,) be an n-dimensional differentiable manifold with a torsion-free linear connection and T*M its cotangent bundle. In this context we study some properties of the natural Riemann extension (M. Sekizawa (1987), O. Kowalski and M. Sekizawa (2011)) on the cotangent bundle T*M. First, we give an alternative definition of the natural Riemann extension with respect to horizontal and vertical lifts. Secondly, we investigate metric connection for the natural Riemann extension. Finally, we present geodesics on the cotangent bundle T*M endowed with the natural Riemann extension. [ABSTRACT FROM AUTHOR]

In Stanciu (Ann Global Anal Geom 56:245-275, 2019), we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of the natural momentum mapping. We use this construction to prove an analogue of a well-known theorem in the symplectic setting about the reduction of cotangent bundles. [ABSTRACT FROM AUTHOR]

Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The aim of this study is to investigate complete lift of vector fields in a special class of semi-tensor bundle tM of the type (p,q). We also have a new example for good square in this work.

Let M be a differentiable manifold, TxM be its tangent space at x ∈ M and TM = {(x, y);x ∈ M;y ∈ TxM} be its tangent bundle. A C0-Finsler structure is a continuous function F : TM → [0, ∞) such that F(x, ⋅) : TxM → [0, ∞) is an asymmetric norm. In this work we introduce the Pontryagin type C0-Finsler structures, which are structures that satisfy the minimum requirements of Pontryagin's maximum principle for the problem of minimizing paths. We define the extended geodesic field ℰ on the slit cotangent bundle T*M\0 of (M, F), which is a generalization of the geodesic spray of Finsler geometry. We study the case where ℰ is a locally Lipschitz vector field. We show some examples where the geodesics are more naturally represented by ℰ than by a similar structure on TM. Finally we show that the maximum of independent Finsler structures is a Pontryagin type C0-Finsler structure where ℰ is a locally Lipschitz vector field. [ABSTRACT FROM AUTHOR]

There are a lot of structures in tangent and cotangent bundle. One of them is the Hsu - (4,2) structure have been defined and studied by Yano, Hough and Chen [1] and the complete and horizontal lifts of Hsu - (4,2) structure extended in Mn to cotangent bundle by R. Nivas and M. Saxena [2]. Hsu-structure had been defined firstly by Prof Mishra [3]. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete and horizontal lifts of Hsu - (4,2) structure. Later, we get the results of Tachibana operators applied to vector and covector fields according to the complete and horizontal lifts of Hsu - (4,2) structure and the conditions of almost holomorfic vector fields in cotangent bundle T *(Mn). Finally, we have studied the purity conditions of Sasakian metric with respect to the lifts of Hsu - (4,2) structure. In the second part, all results obtained in the first section were investigated according to the complete and horizontal lifts of the Hsu - (4,2) structure in tangent bundle T * (Mn). [ABSTRACT FROM AUTHOR]

Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The purpose of this paper is to investigate horizontal lifts of vector fields in a special class of semi-tensor (pull-back) bundle tM of type (p,q). [ABSTRACT FROM AUTHOR]

The framework of the paper is the phase universe, described by the total space of the cotangent bundle of a manifold M, which is of interest for both mathematics and theoretical physics. When M carries a symmetric linear connection, then T ∗ M is endowed with a semi-Riemannian metric, namely the classical Riemann extension, introduced by Patterson and Walker and then by Willmore. We consider here a generalization provided by Sekizawa and Kowalski of this metric, called the natural Riemann extension, which is also a metric of signature (n, n). We give the complete classification of conformal and Killing vector fields with respect to an arbitrary natural Riemann extension. Ricci soliton is a topic that has been increasingly studied lately. Necessary and sufficient conditions for the phase space to become a Ricci soliton (or Einstein) are given at the end. [ABSTRACT FROM AUTHOR]

In this paper, we study a variation in a conjecture of Debarre on positivity of cotangent bundles of complete intersections. We establish the ampleness of Schur powers of cotangent bundles of generic complete intersections in projective manifolds, with high enough explicit codimension and multi-degrees. Our approach is naturally formulated in terms of flag bundles and allows one to reach the optimal codimension. On complex manifolds, this ampleness property implies intermediate hyperbolic properties. We give a natural application of our main result in this context. [ABSTRACT FROM AUTHOR]

This paper consist of three main sections. In the first part, we obtain the complete lifts of the Fa(5, 1)-structure on tangent bundle. We have also obtained the integrability conditions by calculating the Nijenhuis tensors of the complete lifts of Fa(5, 1)-structure. Later we get the conditions of to be the almost holomorfic vector field with respect to the complete lifts of Fa(5, 1)-structure. Finally, we obtained the results of the Tachibana operator applied to the vector fields with respect to the complete lifts of Fa(5, 1)-structure on tangent bundle. In the second part, all results obtained in the first section investigated according to the horizontal lifts of Fa(5, 1)-structure in tangent bundle T(Mn). In finally section, all results obtained in the first and second section were investigated according to the horizontal lifts of the Fa(5, 1)-structure in cotangent bundle T*(Mn). [ABSTRACT FROM AUTHOR]

The Fv+1 - λ²Fv-1 = 0 structure (v ≥ 3) have been studied by Kim J. B. [14]. Later, Srivastava S.K studied on the complete lifts of (1, 1) tensor field F satisfying structure Fv+1 - λ²Fv-1 = 0 and extended in Mn to cotangent bundle. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete and horizontal lifts of Fv+1 - λ²Fv-1 = 0. Later, we get the results of Tachibana operators applied to vector and covector fields according to the complete and horizontal lifts of F ((v+1), λ²(v - 1))-structure and the conditions of almost holomorfic vector fields in cotangent bundle T* (Mn). Finally, we have studied the purity conditions of Sasakian metric with respect to the lifts of Fv+1 - λ²Fv-1 = 0-structure. In the second part, all results obtained in the first section were investigated according to the complete and horizontal lifts of the Fv+1 - λ²Fv-1 = 0 structure in tangent bundle T(Mn). [ABSTRACT FROM AUTHOR]

We prove that the projectivized cotangent bundles of smooth quadrics of dimensions three and four are (p - 1) -th Frobenius split when p > 10 . Besides, we show that the cotangent bundles of certain ordinary elliptic K3 surfaces are not Frobenius split. [ABSTRACT FROM AUTHOR]

We describe a Lefschetz fibration of genus one on the disk cotangent bundle of any closed orientable surface S. As a corollary, we obtain an explicit genus one open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of S. [ABSTRACT FROM AUTHOR]

In this study, the geodesics and torsion tensor according to g-lift of Riemannian connection ▽ on cotangent bundle T*M are investigated. Firstly, using the components of g-lift of Riemannian connection ▽ on cotangent bundle T*M the components of torsion tensor according to glift of Riemannian connection ▽ are obtained. So the torsion tensor according to g-lift of Riemannian connection ▽ are determined. Finally, geodesics on cotangent bundle T*M according to g-lift of Riemannian connection ▽ are studied. [ABSTRACT FROM AUTHOR]

We construct the action of the restricted Weyl group on the set of principal families of orbits of a minimal parabolic subgroup over an algebraically nonclosed field. Additionally, we relate this action to the action on a polarized cotangent bundle. These results generalize the corresponding results of Knop on the action of the Weyl group on the families of Borel orbits of maximal complexity and rank. [ABSTRACT FROM AUTHOR]

Gompf (Ann Math (2) 148(2):619–693, 1998) describes a Stein domain structure on the disk cotangent bundle of any closed surface S by a Legendrian handlebody diagram. We prove that Gompf's Stein domain is symplectomorphic to the disk cotangent bundle equipped with its canonical symplectic structure and the boundary of this domain is contactomorphic to the unit cotangent bundle of S equipped with its canonical contact structure. As a corollary, we obtain a surgery diagram for the canonical contact structure on the unit cotangent bundle of S. [ABSTRACT FROM AUTHOR]

The g-lifts of affine connection and curvature tensor are obtained via the musical isomorphism in the cotangent bundle. [ABSTRACT FROM AUTHOR]

Let (M,ω) be a symplectic manifold. In this paper, the authors consider the notions of musical (bemolle and diesis) isomorphisms ωb: TM → T*M and ω#: T*M → TM between tangent and cotangent bundles. The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ωb-related. As consequence of analyze of connections between the complete lift cωTM of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle, the authors proved that dp is a pullback of cωTM by ω#. Also, the authors investigate the complete lift cϕT*M of almost complex structure ϕ to cotangent bundle and prove that it is a transform by of complete lift cϕTM to tangent bundle if the triple (M, ω,ϕ) is an almost holomorphic A -manifold. The transform of complete lifts of vector-valued 2-form is also studied. [ABSTRACT FROM AUTHOR]

It is known that the cotangent bundle ΩY of an irreducible Hermitian symmetric space Y of compact type is stable. We show that if X ⊂ Y is a subvariety whose structure sheaf has a short split resolution and such that the restriction map Pic(Y ) → Pic(X) is surjective, then, apart from a few exceptions, the restriction ΩY∣X is a stable bundle. We then address some cases where the Picard group increases by restriction. [ABSTRACT FROM AUTHOR]

The kinematical characteristics of distinct infalling homothetic fields are discussed by specifying the transverse subspace of their generated congruences to the energy–momentum deposit of the chosen gravitational system. This is pursued through the inclusion of the base manifold's cotangent bundle in a generalized Raychaudhuri equation and its kinematical expressions. Exploiting an electromagnetic energy–momentum tensor as the source of non-gravitational effects, I investigate the evolution of the mentioned homothetic congruences, as they fall onto a Reissner–Nordström black hole. The results show remarkable differences to the common expectations from infalling congruences of massive particles. [ABSTRACT FROM AUTHOR]

There are many structures in the cotangent bundle. These include the complete and horizontal lifts of the Fλ(7,1) -structure. The F\(7,1) -structure was first extended in Mn to T* (Mn) by Das, Nivas, and Pathak. Later, the horizontal and complete lift of the Fα(K, 1)-structure in the tangent bundle was given by Prasad and Chauhan. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete lifts of the Fλ(7,1) -structure. Later, we get the results of the Tachibana operators applied to vector and covector fields according to the complete lifts of the Fλ(7,1)-structure in the cotangent bundle T* (Mn). Finally, we study the purity conditions of the Sasakian metric with respect to the complete lifts of the Fα(7, 1)-structure. In the second part, all results obtained in the first section are obtained according to the horizontal lifts of the Fα(7, 1)-structure in cotangent bundle T*(Mn). [ABSTRACT FROM AUTHOR]

In the present paper we study paraholomorphy property of the Riemannian extension by using almost paracomplex structure on the cotangent bundle. Then we investigate locally decomposable Golden structure on the cotangent bundle which related to this almost paracomplex structure. [ABSTRACT FROM AUTHOR]

Let (M,g) be a Riemannian manifold equipped with a pair of dual connections (∇,∇*). Such a structure is known as a statistical manifold since it was defined in the context of information geometry. This paper aims at defining the complete lift of such a structure to the cotangent bundle T*M using the Riemannian extension of the Levi-Civita connection of M. In the first section, common tensors are associated with pairs of dual connections, emphasizing the cyclic symmetry property of the so-called skewness tensor. In a second section, the complete lift of this tensor is obtained, allowing the definition of dual connections on TT*M with respect to the Riemannian extension. This work was motivated by the general problem of finding the projective limit of a sequence of a finite-dimensional statistical manifold.

The Black-Scholes partial differential equation (PDE) from mathematical finance has been analysed extensively and it is well known that the equation can be reduced to a heat equation on Euclidean space by a logarithmic transformation of variables. However, an alternative interpretation is proposed in this paper by reframing the PDE as evolving on a Lie group. This equation can be transformed into a diffusion process and solved using mean and covariance propagation techniques developed previously in the context of solving Fokker–Planck equations on Lie groups. An extension of the Black-Scholes theory with coupled asset dynamics produces a diffusion equation on the affine group, which is not a unimodular group. In this paper, we show that the cotangent bundle of a Lie group endowed with a semidirect product group operation, constructed in this paper for the case of groups with trivial centers, is always unimodular and considering PDEs as diffusion processes on the unimodular cotangent bundle group allows a direct application of previously developed mean and covariance propagation techniques, thereby offering an alternative means of solution of the PDEs. Ultimately these results, provided here in the context of PDEs in mathematical finance may be applied to PDEs arising in a variety of different fields and inform new methods of solution.