Screen Almost Semi-Invariant Lightlike Submanifolds of Indefinite Kaehler Manifolds

In the present paper, we introduce screen almost semi-invariant (SASI) lightlike submanifolds of indefinite Keahler manifolds. We obtain the neccesary and sufficient condition for the induced connection to be a metric connection on SASI-lightlike submanifolds and construct an example for this manifold. Also we find some conditions for integrability of distributions and investigate certain characterizations.Comment: 13 page

On the null geometry of quasi generalized CR-submanifolds of indefinite nearly α-Sasakian manifolds.

Master of Science in Pure Mathematics. University of KwaZulu-Natal, Pietermaritzburg 2017.Generalized CR (GCR)-lightlike submanifolds of indefinite almost contact manifolds were introduced by K. L. Duggal and B. Sahin, with the assumption that they are tangent to the structure vector field ξ of the almost contact structure (φ,η,ξ ). Contrary to the above assumption, we have introduced and studied a new class of CR-lightlike submanifold of an indefinite nearly α-Sasakian manifold, called quasi generalized CR (QGCR)-lightlike submanifold. We have showed that QGCR-lightlike submanifold include; ascreen QGCR, co-screen QGCR and the well known GCR-lightlike submanifolds. We have proved some existence (or non-existence) theorems and provided a thorough study of geometry of their distributions. Also, we have constructed many examples, where necessary, to illustrate the main ideas

Generic Lightlike Submanifolds of an Indefinite Cosymplectic Manifold

Lightlike geometry has its applications in general relativity, particularly in black hole theory. Indeed, it is known that lightlike hypersurfaces are examples of physical models of Killing horizons in general relativity (Galloway, 2007). In this paper, we introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold. We investigate new results on a class of generic lightlike submanifolds of an indefinite cosymplectic manifold

Generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a non-metric ϕ-symmetric connection

Jin [13] introduced the notion of non-metric φ-symmetric connection on semi-Riemannian manifolds and studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a non-metric φ-symmetric connection [12]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a non-metric φ-symmetric connection