doiSerbia

Sequential warped products: Curvature and conformal vector fields

De Uday Chand (Department of Pure Mathematics, University of Calcutta, Kolkata, West Bengala, India)
Shenawy Sameh (Basic Science Department, Modern Academy for Engineering and Technology, Maadi, Egypt)
Ünal Bülent (Department of Mathematics, Bilkent University, Bilkent, Ankara, Turkey)

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein’s field equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. Then some important consequences of these formulas are also stated. We provide characterizations of geodesics and two different types of conformal vector fields, namely, Killing vector fields and concircular vector fields on sequential warped product manifolds. Finally, we consider the geometry of two classes of sequential warped product space-time models which are sequential generalized Robertson-Walker space-times and sequential standard static space-times.

Keywords: Warped product manifold, space-times, curvature, Killing vector fields, geodesics, concircular vector fields