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

Mobin Ahmad a , Abdul Haseeb a,∗ and Sheeba Rizvi b

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

Authors :

Mobin Ahmad^a , Abdul Haseeb^a,∗and Sheeba Rizvi^b

Author Address :

^a Department of Mathematics, faculty of science, Jazan University, Jazan, Kingdom of Saudi Arabia.
^bDepartment of Mathematics, Integral University, Kursi Road, Lucknow, India.

*Corresponding author.

Abstract :

We consider an almost $r$-contact Kenmotsu manifold admitting a semi-symmetric metric connection and study semi-invariant submanifolds of an almost $r$-contact Kenmotsu manifold endowed with a semi-symmetric meric connection. We obtain Gauss and Weingarten formuale for such a connection and also discuss the integrability conditions of the distributions on a generalized Kenmotsu manifold.

Keywords :

Kenmotsu manifolds, almost $r$-contact structures, semi-invariant submanifolds, semi-symmetric metric connection, integrability conditions, parallel horizontal distribution.

DOI :

Article Info :

Received : February 06, 2016; Accepted : June 05, 2016.