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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]

In this paper we study the geometry of distributions of semi-slant submanifolds of (α,β) trans-Sasakian manifolds, some problems concerning the stability of slant submanifolds of generalized Sasakian space-forms and we also investigate the first normal Chern class for integral submanifolds of (α,β) trans-Sasakian generalized Sasakian space-forms. [ABSTRACT FROM AUTHOR]

We show geometrical properties of a submanifold of a (LCS)n-manifold. The properties of the induced structures on such a submanifold are also studied. [ABSTRACT FROM AUTHOR]

this article we prove that pseudo-parallel normal antiinvariant submanifolds in Kenmotsu space forms are always semiparallel. [ABSTRACT FROM AUTHOR]

Abstract: In this article, relations between the root space decomposition of a Riemannian symmetric space of compact type and the root space decompositions of its totally geodesic submanifolds (symmetric subspaces) are described. These relations provide an approach to the classification of totally geodesic submanifolds in Riemannian symmetric spaces; this is exemplified by the classification of the totally geodesic submanifolds in the complex quadric obtained in the second part of the article. The classification shows that the earlier classification of totally geodesic submanifolds of by Chen and Nagano (see [B.-Y. Chen, T. Nagano, Totally geodesic submanifolds of symmetric spaces, I, Duke Math. J. 44 (1977) 745–755]) is incomplete. More specifically, two types of totally geodesic submanifolds of are missing from [B.-Y. Chen, T. Nagano, Totally geodesic submanifolds of symmetric spaces, I, Duke Math. J. 44 (1977) 745–755]: The first type is constituted by manifolds isometric to ; their existence follows from the fact that is (via the Segre embedding) holomorphically isometric to . The second type consists of 2-spheres of radius which are neither complex nor totally real in . [Copyright &y& Elsevier]

In this paper, we introduce a new class, called slant lightlike submanifolds, of an indefinite Hermitian manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. As well, we give an example of minimal slant lightlike submanifolds of R28 and prove some characterization theorems. [ABSTRACT FROM AUTHOR]

Cosymplectic manifolds provide a natural setting for time dependent mechanical systems as they are locally product of a Kaehler manifold and a one dimensional manifold. Thus study of warped product submanifolds of cosymplectic manifolds is significant. In this paper we have proved results on the non-existence of warped product submanifolds of certain types in cosymplectic manifolds. [ABSTRACT FROM AUTHOR]

In this paper, the geometry of F-invariant CR-submanifolds of a Kaehlerian product manifold is studied. Fundamental properties of this type submanifolds are investigated such as CR-product, D⊥-totally geodesic and mixed geodesic submanifold. Finally, we have researched totally-umbilical F-invariant proper CR-submanifolds and CR-products in a Kaehlerian product manifold M = M1(c1) × M2(c2). [ABSTRACT FROM AUTHOR]

A theoretical and computational framework for computing intrinsic distance functions and geodesics on submanifolds of ${\Bbb {R}}^d$ given by point clouds is introduced and developed in this paper. The basic idea is that, as shown here, intrinsic distance functions and geodesics on general co-dimension submanifolds of ${\Bbb {R}}^d$ can be accurately approximated by extrinsic Euclidean ones computed inside a thin offset band surrounding the manifold. This permits the use of computationally optimal algorithms for computing distance functions in Cartesian grids. We use these algorithms, modified to deal with spaces with boundaries, and obtain a computationally optimal approach also for the case of intrinsic distance functions on submanifolds of ${\Bbb {R}}^d$. For point clouds, the offset band is constructed without the need to explicitly find the underlying manifold, thereby computing intrinsic distance functions and geodesics on point clouds while skipping the manifold reconstruction step. The case of point clouds representing noisy samples of a submanifold of Euclidean space is studied as well. All the underlying theoretical results are presented along with experimental examples for diverse applications and comparisons to graph-based distance algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this Note is to prove an extension result for positive currents satisfying one of the following conditions: either or one of the currents dT or is of locally finite mass, across of a non-Levi-flat submanifold of class . We prove in the first part that a positive current of dimension p defined in the complement of the zero set of a strictly k-convex function of class () and such that dT is of locally finite mass, is itself of locally finite mass. We recover a result of S. Giret in the case of a Cauchy–Riemann subvariety. To cite this article: K. Dabbek, F. Elkhadhra, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

In this paper, the geometry of F-invariant submanifolds of a Kaehlerian product manifold is studied. The fundamental properties of these submanifolds are investigated such as pseudo umbilical, curvature invariant, totally geodesic, mixed geodesic submanifold and locally decomposable Riemannian product manifold. [ABSTRACT FROM AUTHOR]

We study special Lagrangian cones in &doubleC;n with isolated singularities especially the case n = 3. Our main result constructs an infinite family of special Lagrangian cones in &doubleC;n each of which has a toroidal link. We obtain a detailed geometric description of these toil. We prove a regularity result for special Lagrangian cones in &doubleC;n with a spherical link—any such cone must be a plane. We also construct a one-parameter family of asymptotically conical special Lagrangian submanifolds from any special Lagrangian cone. [ABSTRACT FROM AUTHOR]

We study n-dimensional QR-submanifolds of QR-dimension (p − 1) immersed in a quaternionic space form QP(n+p)/4(c), c ≥ 0, and, in particular, determine such submanifolds with the induced normal almost contact 3-structure. [ABSTRACT FROM AUTHOR]