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In this paper, we establish some general Kastler–Kalau–Walze type theorems for any dimensional manifolds with boundary which generalize the results in [J. Wang and Y. Wang, The Kastler–Kalau–Walze type theorem for six-dimensional manifolds with boundary, J. Math. Phys.56 (2015), Article ID: 052501, 14 pp.]. [ABSTRACT FROM AUTHOR]

We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures. [ABSTRACT FROM AUTHOR]

In this paper we prove the containment I(nm) ⊂ M(n-1)mIm, for a radical ideal I of s general points in Pn, where s ≥ 2n. As a corollary we get that the Chudnovsky Conjecture holds for a very general set of at least 2n points in Pn. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to survey some recent results on the Chern-Moser question concerning existence of umbilical points on three-dimensional CR submanifolds in . [ABSTRACT FROM AUTHOR]

The object of the present paper is to study mixed quasi-Einstein manifolds. Some geometric properties of mixed quasi-Einstein manifolds have been studied. We also discuss spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a mixed quasi-Einstein spacetime. [ABSTRACT FROM AUTHOR]

We derive a formula of the greatest lower bounds on Ricci curvature of Fano homogeneous toric bundles. A criteria for the ampleness of line bundles over general homogeneous toric bundles is also obtained. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study warped product pseudo-slant submanifolds of (LCS)n-manifolds. We study the existence or non-existence of such submanifolds. The existence is also ensured by an example. [ABSTRACT FROM AUTHOR]

In this paper, we study the hemi-slant submanifolds of cosymplectic manifolds. Necessary and sufficient conditions for distributions to be integrable are worked out. Some important results are obtained in this direction. We study the geometry of leaves of hemi-slant submanifolds. [ABSTRACT FROM AUTHOR]

The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the approach of quasi-Einstein manifolds which is directly related to Einstein warped products. In particular, we present an obstruction for the existence of such a class of manifolds. [ABSTRACT FROM AUTHOR]

We extend the canonical cell decomposition due to Epstein and Penner of a hyperbolic manifold with cusps to the strictly convex setting. [ABSTRACT FROM AUTHOR]

We show that an exact Lagrangian cobordism L ⊂ ℝ × P × ℝ from a Legendrian submanifold Λ ⊂ P × ℝ to itself satisfies Hi(L; 픽) = Hi(Λ; 픽) for any field 픽, given that Λ admits a spin exact Lagrangian filling and that the concatenation of any spin exact Lagrangian filling of Λ and L is also spin. The main tool used is Seidel's isomorphism in wrapped Floer homology. In contrast to that, for loose Legendrian submanifolds of ℂn × ℝ, we construct examples of such cobordisms whose homology groups have arbitrarily high ranks. In addition, we prove that the front Sm-spinning construction preserves looseness, which implies certain forgetfulness properties of it. [ABSTRACT FROM AUTHOR]

We consider equivariant wave maps from to in supercritical dimensions . Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable manifold of a self-similar solution with one instability. To probe self-similar blowup, we develop a novel numerical method, based on an adaptive rescaling of coordinates, which may be of independent interest in numerical studies of singularity formation. [ABSTRACT FROM AUTHOR]