Paper · May 30, 2019
Solitonic aspects of submanifolds in Kenmotsu statistical manifolds
As on arXiv
Abstract
The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also been looking into the equation of Ricci soliton and Yamabe soliton in relation with Einstein manifolds, quasi-Einstein manifolds and string theory. In this research article, first we examine the statistical solitons and Yamabe soliton on Kenmotsu statistical manifolds with some related examples. Then we investigate some statistical curvature properties of Kenmotsu statistical manifolds. Also, we study the statistical solitons on submanifolds of Kenmotsu statistical manifold with concircular vector field. Furthermore, we discuss the behavior of almost quasi-Yamabe soliton on submanifolds of Kenmotsu statistical manifolds endowed with concircular vector field and concurrent vector filed. Finally, we furnish an example of -dimensional Kenmotsu statistical manifolds admitting a statistical soliton and almost quasi-Yamabe soliton as well in the support of this study.
- Submitted
- May 30, 2019
- Last revised
- Sep 2, 2023 (v5)
- Subjects
- math.DG
Comments: Some major mistakes are found in this article
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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.