Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(4): 1211-1216

Printed July 31, 2014

https://doi.org/10.4134/BKMS.2014.51.4.1211

Copyright © The Korean Mathematical Society.

On the solutions of the $(\lambda, n+m)$-Einstein equation

Seungsu Hwang

Chung-Ang University

Abstract

In this paper, we study the structure of $m$-quasi Einstein manifolds when there exists another distinct solution to the $(\lambda, n+m)$-Einstein equation. In particular, we derive sufficient conditions for the non-existence of such solutions.

Keywords: Bakry-Emery Ricci tensor, quasi-Einstein manifolds, the $(\lambda, n+m)$-Einstein equation

MSC numbers: Primary 53C21; Secondary 53C25

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