Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds

TL;DR

This paper introduces and analyzes almost Riemann solitons on a special class of almost contact complex Riemannian manifolds derived from cosymplectic manifolds via contact conformal transformations, exploring their curvature properties and providing explicit examples.

Contribution

It studies almost Riemann solitons with vertical potential on conformal cosymplectic contact complex Riemannian manifolds, including curvature analysis and explicit constructions.

Findings

Manifolds classified into four main types based on the studied transformations.

Derived curvature properties of the resulting manifolds.

Constructed explicit five-dimensional example and analyzed Bochner curvature tensor as a conformal invariant.

Abstract

Almost Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e. an almost contact B-metric manifold, obtained from a cosymplectic manifold of the considered type by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The potential of the studied soliton is assumed to be in the vertical distribution, i.e. it is collinear to the Reeb vector field. In this way, manifolds from the four main classes of the studied manifolds are obtained. Curvature properties of the resulting manifolds are derived. An explicit example of dimension five is constructed. The Bochner curvature tensor is used (for dimension at least seven) as a conformal invariant to get properties and construct an explicit example in relation to the obtained results.