Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons

Vladimir Rovenski; Dhriti Sundar Patra

doi:10.3390/fractalfract7020156

Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons

Vladimir Rovenski
, Dhriti Sundar Patra

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This article presents some results of a geometric classification of Sasakian manifolds (SM) that admit an almost ∗-Ricci soliton (RS) structure (Formula presented.). First, we show that a complete SM equipped with an almost ∗-RS with (Formula presented.) const is a unit sphere. Then we prove that if an SM has an almost ∗-RS structure, whose potential vector is a Jacobi vector field on the integral curves of the characteristic vector field, then the manifold is a null or positive SM. Finally, we characterize those SM represented as almost ∗-RS, which are ∗-RS, ∗-Einstein or ∗-Ricci flat.

Original language	English
Article number	156
Journal	Fractal and Fractional
Volume	7
Issue number	2
DOIs	https://doi.org/10.3390/fractalfract7020156
State	Published - Feb 2023

Bibliographical note

Publisher Copyright:
© 2023 by the authors.

Keywords

(almost) ∗-Ricci soliton
conformal vector field
infinitesimal contact transformation
sasakian manifold
∗-Einstein manifold

ASJC Scopus subject areas

Analysis
Statistical and Nonlinear Physics
Statistics and Probability

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10.3390/fractalfract7020156

Cite this

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title = "Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons",

abstract = "This article presents some results of a geometric classification of Sasakian manifolds (SM) that admit an almost ∗-Ricci soliton (RS) structure (Formula presented.). First, we show that a complete SM equipped with an almost ∗-RS with (Formula presented.) const is a unit sphere. Then we prove that if an SM has an almost ∗-RS structure, whose potential vector is a Jacobi vector field on the integral curves of the characteristic vector field, then the manifold is a null or positive SM. Finally, we characterize those SM represented as almost ∗-RS, which are ∗-RS, ∗-Einstein or ∗-Ricci flat.",

keywords = "(almost) ∗-Ricci soliton, conformal vector field, infinitesimal contact transformation, sasakian manifold, ∗-Einstein manifold",

author = "Vladimir Rovenski and Patra, \{Dhriti Sundar\}",

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doi = "10.3390/fractalfract7020156",

language = "English",

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journal = "Fractal and Fractional",

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T1 - Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons

AU - Rovenski, Vladimir

AU - Patra, Dhriti Sundar

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N2 - This article presents some results of a geometric classification of Sasakian manifolds (SM) that admit an almost ∗-Ricci soliton (RS) structure (Formula presented.). First, we show that a complete SM equipped with an almost ∗-RS with (Formula presented.) const is a unit sphere. Then we prove that if an SM has an almost ∗-RS structure, whose potential vector is a Jacobi vector field on the integral curves of the characteristic vector field, then the manifold is a null or positive SM. Finally, we characterize those SM represented as almost ∗-RS, which are ∗-RS, ∗-Einstein or ∗-Ricci flat.

AB - This article presents some results of a geometric classification of Sasakian manifolds (SM) that admit an almost ∗-Ricci soliton (RS) structure (Formula presented.). First, we show that a complete SM equipped with an almost ∗-RS with (Formula presented.) const is a unit sphere. Then we prove that if an SM has an almost ∗-RS structure, whose potential vector is a Jacobi vector field on the integral curves of the characteristic vector field, then the manifold is a null or positive SM. Finally, we characterize those SM represented as almost ∗-RS, which are ∗-RS, ∗-Einstein or ∗-Ricci flat.

KW - (almost) ∗-Ricci soliton

KW - conformal vector field

KW - infinitesimal contact transformation

KW - sasakian manifold

KW - ∗-Einstein manifold

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DO - 10.3390/fractalfract7020156

M3 - Article

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SN - 2504-3110

VL - 7

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 2

M1 - 156

ER -

Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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