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(3): 839-849

Online first article May 13, 2022      Printed July 31, 2022

https://doi.org/10.4134/CKMS.c210097

Copyright © The Korean Mathematical Society.

New volume comparison with almost Ricci soliton

Shahroud azami, Sakineh Hajiaghasi

Imam Khomeini International University; Imam Khomeini International University

Abstract

In this paper we consider a condition on the Ricci curvature involving vector fields which enabled us to achieve new results for volume comparison and Laplacian comparison. These results in special case obtained with considering volume non-collapsing condition. Also, by applying this condition we get new results of volume comparison for almost Ricci solitons.

Keywords: Volume comparison, Bakry-'{E}mery Ricci curvature

MSC numbers: 53C21, 58C25

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