# IJPAM: Volume 88, No. 3 (2013)

SOME PROPERTIES OF -QUASI
EINSTEIN MANIFOLDS

Jaeman Kim
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 .

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