A Study of Kenmotsu-like Statistical Submersions

Siddiqi, Mohd Danish; Siddiqui, Aliya Naaz; Mofarreh, Fatemah; Aytimur, Hülya

doi:10.3390/sym14081681

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…Similar to the Takano's results in [38] and Aytimur and Ozgur's results in [6], Danish, the first author, Mofarreh and Aytimur [33] examine that, for Kenmotsu-like statistical submersion ω, the base space (N, ∇, g N , J) is a Kähler-like statistical manifold and each fiber (M , ∇, g, ϕ, ξ, η) is a Kenmotsu-like statistical manifold (see Theorems 3.24 and 3.30). Secondly, they study Kenmotsu-like statistical submersions admit the axioms that the curvature tensor with respect to the affine connection ′ ∇ of M follows certain conditions (see Theorems 3.26, 3.27).…”

Section: Definition 18 [33] a Statistical Submersionsupporting

confidence: 85%

“…He derives interesting properties of such statistical submersions [39]. Similar to the Takano's definition for Sasaki-like statistical submersion, Danish, Siddiqui and Aytimur define and discuss nice properties of Kenmotsu-like statistical submersion in [33]. Also, they study Kenmotsu-like statistical submersions with conformal fibers.…”

Section: Holds For Any E F G ∈ γ(T M )mentioning

confidence: 89%

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A study of statistical submersions

Siddiqui

Ahmad²

2023

Tamkang J. Math.

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In the sixties, A. Gray \cite{Gr} and B. O'Neill \cite{O1} come with the notion of Riemannian submersions as a tool to study the geometry of a Riemannian manifold with an additional structure in terms of the fibers and the base space. Riemannian submersions have long been an effective tool to construct Riemannian manifolds with positive or nonnegative sectional curvature in Riemannian geometry and compare certain manifolds within differential geometry. In particular, many examples of Einstein manifolds can be constructed by using such submersions. It is very well known that Riemannian submersions have applications in physics, for example Kaluza-Klein theory, Yang-Mills theory, supergravity and superstring theories.

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Section: Definition 18 [33] a Statistical Submersionsupporting

confidence: 85%

Section: Holds For Any E F G ∈ γ(T M )mentioning

confidence: 89%

A study of statistical submersions

Siddiqui

Ahmad²

2023

Tamkang J. Math.

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“…For this reason, the geometric study of statistical submersions is new and has many research problems. Therefore, we believe that the present article will help in achieving new and interesting results in the geometry of statistical solitons [35] on statistical submersions [36]. In fact, some singularity theories on submanifolds can be studied [14][15][16][17].…”

Section: Conclusion and Remarkmentioning

confidence: 76%

Conformal η-Ricci Solitons on Riemannian Submersions under Canonical Variation

Siddiqi

Alkhaldi

Khan

et al. 2022

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This research article endeavors to discuss the attributes of Riemannian submersions under the canonical variation in terms of the conformal η-Ricci soliton and gradient conformal η-Ricci soliton with a potential vector field ζ. Additionally, we estimate the various conditions for which the target manifold of Riemannian submersion under the canonical variation is a conformal η-Ricci soliton with a Killing vector field and a φ(Ric)-vector field. Moreover, we deduce the generalized Liouville equation for Riemannian submersion under the canonical variation satisfying by a last multiplier Ψ of the vertical potential vector field ζ and show that the base manifold of Riemanian submersion under canonical variation is an η Einstein for gradient conformal η-Ricci soliton with a scalar concircular field γ on base manifold. Finally, we illustrate an example of Riemannian submersions between Riemannian manifolds, which verify our results.

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“…The research of Ricci solitons, Yamabe solitons, and their variants in diverse geometric contexts has gained significant traction over the last two decades, with applications in fields such as general relativity, applied mathematics, and theoretical physics. These investigations have been extended to almost contact manifolds, including work by Nagaraja and Premalatha [15], Blaga [16,17], Calin [18], Danish [19,20], Aliya et al [21][22][23], and others [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Statistical Solitonic Impact on Submanifolds of Kenmotsu Statistical Manifolds

Ahmadini,

Siddiqi,

Siddiqui

2024

Mathematics

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In this article, we delve into the study of statistical solitons on submanifolds of Kenmotsu statistical manifolds, introducing the presence of concircular vector fields. This investigation is further extended to study the behavior of almost quasi-Yamabe solitons on submanifolds with both concircular and concurrent vector fields. Concluding our research, we offer a compelling example featuring a 5-dimensional Kenmotsu statistical manifold that accommodates both a statistical soliton and an almost quasi-Yamabe soliton. This example serves to reinforce and validate the principles discussed throughout our study.

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A Study of Kenmotsu-like Statistical Submersions

Cited by 6 publications

References 25 publications

A study of statistical submersions

A study of statistical submersions

Conformal η-Ricci Solitons on Riemannian Submersions under Canonical Variation

Statistical Solitonic Impact on Submanifolds of Kenmotsu Statistical Manifolds

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