Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2023; 60(3): 763-774

Online first article May 16, 2023      Printed May 31, 2023

https://doi.org/10.4134/BKMS.b220366

Copyright © The Korean Mathematical Society.

Bach almost solitons in paraSasakian geometry

Uday Chand De, Gopal Ghosh

University of Calcutta; Cooch Behar Government Engineering College

Abstract

If a paraSasakian manifold of dimension $(2n+1)$ represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric $g$ has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if $r=-6$; shrinking if $r>-6$; expanding if $r<-6$.

Keywords: Bach tensor, Cotton tensor, paraSasakian manifold

MSC numbers: Primary 53C15, 53C25

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