Sequential Warped Product Manifolds With a Semi-Symmetric Metric Connection

Abstract

In the present paper, we study a new generalization of warped product
manifolds, called sequential warped product manifolds, with respect to a
semi-symmetric metric connection. We obtain relations for covariant
derivatives, Riemannian curvature, Ricci curvature and scalar curvature of the
sequential warped product manifolds with respect to the semi-symmetric
connection, respectively, and demonstrate the relationship between them and
curvatures with respect to the Levi-Civita connection. Also, we consider
sequential warped product space-time models, namely sequential generalized
Robertson-Walker space-times and sequential standard static space-times, with
semi-symmetric metric connections and obtain conditions for such space-times
to be Einstein.