IJPAM: Volume 88, No. 3 (2013)
EINSTEIN MANIFOLDS
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
Year: 2013
Volume: 88
Issue: 3