Version 1
: Received: 23 May 2024 / Approved: 23 May 2024 / Online: 23 May 2024 (14:16:19 CEST)
How to cite:
MANEV, M. Ricci–Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds. Preprints2024, 2024051569. https://doi.org/10.20944/preprints202405.1569.v1
MANEV, M. Ricci–Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds. Preprints 2024, 2024051569. https://doi.org/10.20944/preprints202405.1569.v1
MANEV, M. Ricci–Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds. Preprints2024, 2024051569. https://doi.org/10.20944/preprints202405.1569.v1
APA Style
MANEV, M. (2024). Ricci–Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds. Preprints. https://doi.org/10.20944/preprints202405.1569.v1
Chicago/Turabian Style
MANEV, M. 2024 "Ricci–Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds" Preprints. https://doi.org/10.20944/preprints202405.1569.v1
Abstract
Almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here we consider a special class of these manifolds, those of the Sasaki-like type. They have an interesting geometric interpretation: the complex cone of such a manifold is a holomorphic complex Riemannian manifold (also called a Kähler–Norden manifold). The basic metric on the considered manifold is specialized here as a soliton, i.e. has an additional curvature property such that the metric is a self-similar solution of an intrinsic geometric flow. Almost solitons are more general objects than solitons because they use functions rather than constants as coefficients in the defining condition. A β -Ricci-Bourguignon-like almost soliton ( β is a real constant) is defined using the pair of metrics. The introduced soliton is a generalization of some well-known (almost) solitons (such as those of Ricci, Schouten, Einstein), which in principle arise from a single metric rather than a pair of metrics. The soliton potential is chosen to be pointwise collinear to the Reeb vector field, or the Lie derivative of any B-metric along the potential to be the same metric multiplied by a function. The resulting manifolds equipped with the introduced almost solitons are characterized geometrically. Appropriate examples for two types of almost solitons are constructed and the properties obtained in the theoretical part are confirmed.
Keywords
Ricci–Bourguignon; almost contact B-metric manifold; almost contact complex Riemannian manifold; Sasaki-like manifold; vertical potential; conformal potential
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.
