IJPAM: Volume 67, No. 4 (2011)
SOME SPECIAL RIEMANNIAN MANIFOLDS
Department of Mathematics
Faculty of Sciences and Letters
Istanbul Technical University
Maslak, Istanbul, 34469, TURKEY
Abstract. The purpose of this paper is to study some properties of the Schouten tensor arising from the considerations of conformal geometry.
In the special cases when the Schouten tensor is recurrent, generalized recurrent and generalized 2-recurrent, it is found the conditions over the manifold. Additionally, in a Riemannian manifold with the constant curvature, it is proved that the Schouten tensor is an Einstein tensor.
In the last section of this paper, an example is given for the existence of the Schouten tensor for a 4-dimensional Riemannian manifold.
Received: January 13, 2011
AMS Subject Classification: 53C15, 53C25,53B15, 53B20
Key Words and Phrases: Schouten tensor, recurrent manifold, generalized recurrent manifold, generalized Ricci-recurrent manifold, quasi-constant curvature, Killing vector, quadratic conformal Killing tensor
Source: International Journal of Pure and Applied Mathematics