semi-Riemannian Product Research Articles

Screen generic lightlike submanifolds of semi-Riemannian product manifolds

In this paper, we introduce screen generic lightlike submanifolds of semi-Riemannian product manifolds. We investigate the integrability of various distributions and geometry of such submanifolds. Finally, we find a condition for minimal screen generic lightlike submanifolds. We also give examples.

Geometry and holonomy of indecomposable cones

We study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product. This includes irreducible cones, for which the holonomy can be classified, as well as non irreducible cones. The latter admit a parallel distribution of null $k$-planes, and we study the cases $k=1$ in detail. We give structure theorems about the base manifold and in the case when the base manifold is Lorentzian, we derive a description of the cone holonomy. This result is obtained by a computation of certain cocycles of indecomposable subalgebras in $\mathfrak{so}(1,n-1)$.

A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS

We study GCR-lightlike submanifolds of semi-Riemannian product manifolds. We give some equivalent conditions for the integrability of various distributions of GCR-lightlike submanifolds of semi-Riemannian product manifolds and investigate the geometry of leaves of distributions.

On the Angle of Complete Hypersurfaces in Semi-Riemannian Product Spaces

The purpose of this article is to study the uniqueness of complete hypersurfaces satisfying some pinching curvature condition. Here, we use the generalized maximum principle of Omori–Yau to obtain uniqueness results for complete spacelike hypersurfaces immersed in a Lorentzian product space. In addition, we obtain the analogue results for complete hypersurfaces immersed in a Riemannian product space.

Para-contact product semi-Riemannian submersions

We introduce the concept of para-contact product semi-Riemannian submersions from an almost para-contact metric manifold onto a semi-Riemannian product manifold. We provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost para-contact structure of the total manifold. Moreover, we investigate various properties of the O’Neill’s tensors of such submersions, fnd the integrability of the horizontal distribution. The paper is also focused on the transference of structures defined on the total manifold

Lightlike Submanifolds with Planar Normal Section in Semi Riemannian Product Manifolds

In the present paper we give conditions for screen semi invariant lightlike submanifolds of a semi- Riemannian product manifold to have degenerate planar normal sections. Also we give sufficient and efficient conditions for screen invariant and screen anti invariant lightlike submanifold of a semi-Riemanniann product manifold to have non-degenerate planar normal sections.

Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection

We study lightlike submanifolds of a semi-Riemannian product manifold. We introduce a class of lightlike submanifolds called screen semi-invariant lightlike submanifold. We consider lightlike submanifolds with respect to a quarter symmetric non-metric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

RADICAL SCREEN TRANSVERSAL LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS

We study screen transversal lightlike submanifolds of semi-Riemannian product manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also obtain characterization of screen transversal anti-invariant lightlike submanifolds.

GCR-LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN PRODUCT MANIFOLD

We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical anti-invariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quarter-symmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

Totally Umbilical Screen Transversal Lightlike Submanifolds of Semi-Riemannian Product Manifolds

We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.

Semi-invariant lightlike submanifolds of a semi-Riemannian product manifold

In this paper, we introduce a new class of lightlike submanifolds, namely, semi-invariant lightlike submanifolds of a semi-Riemannian product manifold. We investigate totally umbilical, curvature invariant lightlike submanifolds in real space forms M1(c1) × M2(c2) and discuss integrabilities of distributions on semi-Riemannian product manifold.