Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold

Abstract

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a lightlike hypersurface. In addition to these main theorems, we study the geometry of totally geodesic lightlike hypersurfaces of an indefinite Sasakian manifold.

Half Lightlike Submanifolds of an Indefinite Sasakian Manifold

“…We proved lightlike hypersurface version of the above classical result: If a locally symmetric lightlike hypersurface of an indefinite Sasakian manifold is totally geodesic, then it is of constant positive curvature 1 [5].…”

Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

“…As ∇ ⊥ = ( ) , we show that the transversal connection of is flat if and only if the 1-form is closed; that is, = 0, on any U ⊂ [3]. Denote and by the 1-forms such that …”

“…Cȃlin [8] proved that if is tangent to , then it belongs to ( ) which we assume in this paper. It is well known [3,6] that, for any lightlike hypersurface of an indefinite almost contact metric manifold , ( ⊥ ) and (tr( )) are subbundles of ( ), of rank 1, and…”

“…Recently author has been studying the geometry of lightlike hypersurfaces of indefinite Sasakian [3], Kenmotsu [4], and cosymplectic [5] manifolds. In this paper, we study lightlike hypersurfaces of an indefinite generalized Sasakian space form ( 1 , 2 , 3 ), with indefinite transSasakian structure of type ( , ), subject to the condition that the structure vector field of is tangent to .…”

LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM WITH A SYMMETRIC METRIC CONNECTION OF TYPE (ℓ, m)

“…It is known [9] that, for any lightlike hypersurface M of an indefinite almost contact metric manifoldM , J(T M ⊥ ) and J(tr(T M )) are subbundles of S(T M ), of rank 1. In the entire discussion of this article, we shall assume that ζ is tangent to M .…”