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Pairs of Associated Yamabe Almost Solitons with Vertical Potential on Almost Contact Complex Riemannian Manifolds
Version 1
: Received: 2 June 2023 / Approved: 2 June 2023 / Online: 2 June 2023 (14:33:49 CEST)
A peer-reviewed article of this Preprint also exists.
Manev, M. Pairs of Associated Yamabe Almost Solitons with Vertical Potential on Almost Contact Complex Riemannian Manifolds. Mathematics 2023, 11, 2870. Manev, M. Pairs of Associated Yamabe Almost Solitons with Vertical Potential on Almost Contact Complex Riemannian Manifolds. Mathematics 2023, 11, 2870.
Abstract
Almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds, are in principle equipped with a pair of mutually associated pseudo-Riemannian metrics. Each of these metrics is specialized here as a Yamabe almost soliton with a potential collinear to the Reeb vector field. The resulting manifolds are then investigated in two important cases with geometric significance. The first is when the manifold is of Sasaki-like type, i.e. its complex cone is a holomorphic complex Riemannian manifold (also called a Kähler–Norden manifold). The second case is when the soliton potential is torse-forming, i.e. it satisfies a certain recurrence condition for its covariant derivative with respect to the Levi-Civita connection of the corresponding metric. The studied solitons are characterized. In the three-dimensional case, an explicit example is constructed and the properties obtained in the theoretical part are confirmed.
Keywords
Yamabe soliton; almost contact B-metric manifold; almost contact complex Riemannian manifold; Sasaki-like manifold; torse-forming vector field
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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