Communications of the
Korean Mathematical Society
CKMS

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

Article

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Commun. Korean Math. Soc. 2022; 37(4): 1199-1207

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

https://doi.org/10.4134/CKMS.c210336

Copyright © The Korean Mathematical Society.

Riemannian submersions whose total space is endowed with a torse-forming vector field

\c{S}emsi Eken~Meri\c{c}, Erol K{\i}l{\i}\c{c}

Mersin University; İnönü University

Abstract

In the present paper, a Riemannian submersion $\pi$ between Riemannian manifolds such that the total space of $\pi$ endowed with a torse-forming vector field $\nu$ is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of $\pi$ or the base manifold $B$ to be an almost quasi-Einstein are obtained.

Keywords: Ricci soliton, Riemannian submersion, torse-forming vector field

MSC numbers: Primary 53C25, 53C42

Supported by: This work is supported by 1001-Scientific and Technological Research Projects Funding Program of TUBITAK project number 117F434.