As on arXiv
Abstract
Recent interest among geometers in -structures of K. Yano is due to the study of topology and dynamics of contact foliations and generalized A. Weinstein conjectures. Weak metric -structures, introduced by the author and R. Wolak as a generalization of Hermitian structure, as well as -structure allow for a fresh perspective on the classical theory. An important case of such manifolds, which is locally a twisted product, is a weak -Kenmotsu manifold defined as a generalization of K. Kenmotsu's concept. In this paper, the concept of the -Ricci tensor of S. Tashibana is adapted to weak metric -manifolds, the interaction of --Ricci soliton with the weak -Kenmotsu structure is studied and new characteristics of -Einstein metrics are obtained.
Comments: 18 pages. arXiv admin note: text overlap with arXiv:2503.18031, arXiv:2412.14125
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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-Ricci solitons and -Einstein metrics on weak -Kenmotsu -manifolds
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Einstein metrics · Same author Vladimir Rovenski · Shared terms “Kenmotsu”, “weak metric”, “contact foliations”
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--Ricci solitons and Einstein metrics on a weak -Kenmotsu manifold
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Einstein metrics · Same author Vladimir Rovenski · Shared terms “Kenmotsu”, “manifold defined”, “twisted product”
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Einstein-type metrics and generalized Ricci solitons on weak -K-contact manifolds
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Einstein metrics · Same author Vladimir Rovenski · Shared terms “weak metric”, “Ricci tensor”, “foliation”
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Generalized Ricci solitons and Einstein metrics on weak -contact manifolds
Topics Sasakian & contact geometry, Einstein metrics, Ricci solitons · Same author Vladimir Rovenski · Shared terms “classical theory”, “Ricci tensor”
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Kenmotsu metric as conformal -Ricci soliton
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “Kenmotsu”, “Einstein”
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-Ricci Solitons on Kenmotsu 3-Manifolds
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “Kenmotsu”, “Ricci tensor”
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Back to almost Ricci solitons
Topics Almost & η-Ricci solitons, Einstein metrics, Ricci solitons · Same author Vladimir Rovenski · Shared terms “Ricci tensor”
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Characterizations of weak almost -manifolds with curvature properties
Topics Sasakian & contact geometry · Same author Vladimir Rovenski · Shared terms “weak metric”, “Wolak”, “Yano”
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.