On Geometry of Submanifolds of (LCS)n-Manifolds

The geometry of manifolds endowed with geometrical structures has been intensively studied, and several important results have been published. In this paper, we deal with manifolds having a Lorentzian concircular structure LCS n-manifold 1–3 see Section 2 for detail . The study of the Lorentzian almost paracontact manifold was initiated by Matsumoto in 4 . Later on, several authors studied the Lorentzian almost paracontact manifolds and their different classes including 1, 4, 5 . Recently, the notion of the Lorentzian concircular structure manifolds was introduced in briefly LCS -manifolds with an example, which generalizes the notion of the LP-Sasakian manifolds introduced by Matsumoto in 4 . Papers related to this issue are very few in the literature so far. But the geometry of submanifolds of a LCS -manifold is rich and interesting. So, in the present paper we introduce the concept of submanifolds of a LCS -manifold and investigate the fundamental properties of such submanifolds. We obtain the necessary and sufficient conditions for a submanifold of LCS -manifold to be invariant. In this case, the induced structures on submanifold by the structure on ambient space are classified. I think that the results will contribute to geometry.