Doubly warped product manifolds with respect to a semi-symmetric non-metric connection

Abstract

The main goal of the present paper is to get new equalities with respect to a special connection titled ‘’Semisymmetric non-metric connection’’. Whoever wants to study manifol or submanifold theory with this type of special connection, our new equalities can be used in the future studies. In this study, we calculate Koszul formulas on doubly warped product manifolds endowed with the semi-symmetric non-metric connection and we give relations between Levi-Civita connection and semi-symmetric non-metric connection of a doubly warped product manifold M=f B×b F. We also get some results of Einstein doubly warped product manifolds with a semi-symmetric non-metric connection.