Almost Yamabe Solitons on a Total Space of Almost Hermitian Submersions

TL;DR

This paper investigates the properties of almost Yamabe solitons on the total space of almost Hermitian submersions, especially focusing on Kaehler submersions, and characterizes their behavior under various geometric conditions.

Contribution

It provides new characterizations of almost Yamabe solitons on submersions, including conditions for shrinking, steady, and expanding types, and explores special cases like Yamabe solitons.

Findings

Fibres and base manifolds can be almost Yamabe solitons under certain conditions.

Characterizations of soliton types in terms of extrinsic horizontal scalar curvature.

Results on behavior of vector fields and special cases like Yamabe solitons.

Abstract

This article presents the study of almost Hermitian submersion from an almost Yamabe soliton onto an almost Hermitian manifold. A non-trivial example is also mentioned in order to guarantee the existence of such solitons on the total space of almost Hermitian submersions. We mainly focus on Kaehler submersions from Kaehler manifolds which are special case of almost Hermitian submersions. Under certain conditions, we find out that the fibres and the base manifold of such submersions are almost Yamabe soliton. We give the characterizations for an almost Yamabe soliton of a Kaehler submersion to be shrinking, steady and expanding in terms of extrinsic horizontal scalar curvature. Moreover, we observe the behavior of torqued, recurrent and concurrent vector field of the total space of the Kaehler submersion. In particular, we obtain characterization for an almost Yamabe soliton consisting of concurrent vector fields. Meanwhile, we give some results of such submersions when the total space is Yamabe soliton which is a particular case of almost Yamabe soliton.