IJPAM: Volume 88, No. 3 (2013)
Department of Mathematics Education
Kangwon National University
Chunchon, 200-701, KOREA
Abstract. In this paper, an example of an -quasi Einstein manifold with closed associated 1-form is given. Also we show that if a quasi Einstein manifold and an Einstein manifold satisfy a certain condition, then the Riemannian product manifold is a quasi Einstein manifold. In particular, in -quasi Einstein case, we show that there exists a quasi Einstein product manifold but not an -quasi Einstein manifold, which consists of an -quasi Einstein manifold and an Einstein manifold satisfying the certain condition. Finally we study an -quasi Einstein manifold satisfying the condition .
Received: May 16, 2013
AMS Subject Classification: 53A30, 53A40, 53B20
Key Words and Phrases: quasi Einstein manifold, associated 1-form, -quasi Einstein manifold, Riemannian product manifolds, quasi Einstein product manifold, G-curvature tensor, Killing vector field, Ricci-semisymmetric manifold
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DOI: 10.12732/ijpam.v88i3.3 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395