Yamabe Solitons on Conformal Almost Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field

TL;DR

This paper investigates Yamabe solitons on a special class of almost contact complex Riemannian manifolds, focusing on those with a vertical torse-forming vector field, and provides explicit examples and classifications.

Contribution

It introduces a study of Yamabe solitons with vertical torse-forming vector fields on conformally transformed almost contact B-metric manifolds, including explicit examples.

Findings

Identification of a main class of manifolds with Yamabe solitons and vertical torse-forming vector fields.

Explicit 5-dimensional Lie group example related to the theoretical results.

Characterization of manifolds obtained via contact conformal transformations and their properties.

Abstract

A Yamabe soliton is considered on an almost contact complex Riemannian manifold (also known as an almost contact B-metric manifold) which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The case when the potential is a torse-forming vector field of constant length on the vertical distribution determined by the Reeb vector field is studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the given B-metric. An explicit 5-dimensional example of a Lie group is given, which is characterized in relation to the obtained results.