IJPAM: Volume 67, No. 4 (2011)

ON THE SCHOUTEN TENSOR OF
SOME SPECIAL RIEMANNIAN MANIFOLDS

Füsun Özen Zengin
Department of Mathematics
Faculty of Sciences and Letters
Istanbul Technical University
Maslak, Istanbul, 34469, TURKEY
e-mail: [email protected]


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
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 4