Totally and C-Totally Real Submanifolds of Sasakian Manifolds and Sasakian Space Forms

Abstract

In the present paper, we study totally real submanifolds of Sasakian manifolds. Also, we study totally and C-totally real submanifolds of Sasakian space forms with respect to Levi-Civita connection as well as quarter symmetric metric connection. We have obtained some results in this regard. Among these results, we have made an important deduction that the scalar curvatures of a C-totally real submanifold of a Sasakian space form with respect to both the aforesaid connections are the same.

Key words and phrases. Totally real submanifold, C-totally real submanifold, Sasakian manifold, Sasakian space form, quarter symmetric metric connection.

2010 Mathematics Subject Classification. 53C15, 53C20, 53C25, 53C40