On Einstein warped products with a quarter-symmetric connection

Abstract

This paper characterizes the warping functions for a multiply generalized Robertson–Walker space-time to get an Einstein space [Formula: see text] with a quarter-symmetric connection for different dimensions of [Formula: see text] (i.e. (1). dim [Formula: see text] (2). dim [Formula: see text]) when all the fibers are Ricci flat. Then we have also computed the warping functions for a Ricci flat Einstein multiply warped product spaces M with a quarter-symmetric connection for different dimensions of [Formula: see text] (i.e. (1). dim [Formula: see text] (2). dim [Formula: see text] (3). dim [Formula: see text]) and all the fibers are Ricci flat. In the last section, we have given two examples of multiply generalized Robertson–Walker space-time with respect to quarter-symmetric connection.

A family of multiply warped product semi-Riemannian Einstein metrics

“…In 2012, authors [14] described warped product Einstein metrics when the base is locally conformally flat. In ( [16], [17]), authors studied Ricci flat Einstein warped product space and Einstein warped product space with quarter symmetric connection. In 2000, B. Unal [19] derived covariant derivative formulas for multiply warped products and also studied the geodesic equations for such type of spaces.…”

“…and equation (3) again will convert into equation (17). Hence from ( 16) and (18) we get the first equation of (11).…”

Study on Einstein Warped Product space with Quarter Symmetric Connection

“…In [12] they have studied warped products and multiply warped product on quasi-Einstein manifolds with a quarter symmetric connection. After that in 2017 [13], they have also characterizes the warping function for a multiply generalized Robertson-Walker space-time to get an Einstein space M with a quarter symmetric connection for different dimension of M . Motivated from the above papers arrangement of this paper follows as, In section 2, we give the definition of semi-symmetric, quarter symmetric connection after that give the formula for curvature, Ricci and scalar tensor with respect to quarter symmetric connection.…”

Killing forms on Riemannian Poisson warped product space

“…To provide the example of Riemannian spaces having negative curvature Bishop and O'Neill [1] introduced the notion of warped space. From then on original and generalized form of warped product spaces have been widely discussed by both mathematicians and physicists [2,3,4,5,6,7,8,9].…”