HYPERSURFACES OF ALMOST Γ-Paracontact RIEMANNIAN MANIFOLD ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTION

Abstract

Abstract. We define a semi-symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

Semi-invariant submanifolds of a Kenmotsu manifold with a generalized almost r-contact structure admitting a semi-symmetric metric connection

“…On the other hand, A. Bejancu, introduced the notion of semi-invariant submanifolds [6] or contact CR-submanifolds [5], as a generalization of invariant and anti-invariant submanifolds of an almost contact metric manifold and was followed by several geometers in [1,2,4,7,11,12]. Semi-invariant submanifolds of a Kenmotsu manifold immersed in a generalized almost r-contact metric structure was defined and studied by R. Nivas and S. Yadav [13].…”

Hypersurfaces of an almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Non-metric Connection

“…Hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection were studied by J. B. Jun and the first author in [9]. Hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection were studied by first and second author in [1].…”

SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A SEMI-SYMMETRIC METRIC CONNECTION

“…where X and Y are vector fields on M , then the structure = (φ, ξ α , η α , g) α∈(r) is said to be an almost r-paracontact Riemannian structure and M is an almost r-paracontact Riemannian manifold [8].…”

“…In [16], K. Yano considered a semi-symmetric metric connection and studied some of its properties. In [1], [2], [3], [6], [7], [8], [9] and [14], some kinds of semi-symmetric metric or non-metric connections were studied.…”