Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2022; 37(2): 631-634

Online first article April 12, 2022      Printed April 30, 2022

https://doi.org/10.4134/CKMS.c210171

Copyright © The Korean Mathematical Society.

A note on static manifolds and almost Ricci solitons

Reihaneh Ahmadzadeh, Hajar Ghahremani-Gol

Shahed University; Shahed University

Abstract

In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.

Keywords: Almost Ricci solitons, constant scalar curvature, static manifolds

MSC numbers: 53C21, 53C44, 53C25

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