Minimal Legendrian submanifolds in Sasakian space forms with C-parallel second fundamental form

Xing, Cheng; Zhai, Shujie

doi:10.1016/j.geomphys.2023.104790

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…for any arbitrary X 0 , Y 0 , Z 0 and W 0 belonging to M 2k+1 . For more detail, go to [29][30][31][32][33]. The Gauss equation is defined as:…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms

Li,

Mofarreh,

Abolarinwa

et al. 2023

Mathematics

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This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the q-Laplacian. In particular, various estimates are provided for the first eigenvalue of the q-Laplace operator on closed orientated (l+1)-dimensional special contact slant submanifolds in a Sasakian space form, M˜2k+1(ϵ), with a constant ψ1-sectional curvature, ϵ. From our main results, we recovered the Reilly-type inequalities, which were proven before this study.

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“…for any arbitrary X 0 , Y 0 , Z 0 and W 0 belonging to M 2k+1 . For more detail, go to [29][30][31][32][33]. The Gauss equation is defined as:…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms

Li,

Mofarreh,

Abolarinwa

et al. 2023

Mathematics

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show abstract

“…The geometry of these manifolds is more meaningful. In the theory of Riemannian spaces, spaces with other structures that arise in theoretical physics play an important role, especially Kähler and Sasaki spaces, and their generalizations, see [6][7][8][9][10][11][12]. The properties of the geometry of such spaces are richer in content.…”

Section: Introductionmentioning

confidence: 99%

Geometry of Harmonic Nearly Trans-Sasakian Manifolds

Rustanov

2023

Axioms

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This paper considers a class of nearly trans-Sasakian manifolds. The local structure of nearly trans-Sasakian structures with a closed contact form and a closed Lee form is obtained. It is proved that the class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coincides with the class of almost contact metric manifolds with a closed contact form locally conformal to the closely cosymplectic manifolds. A wide class of harmonic nearly trans-Sasakian manifolds has been identified (i.e., nearly trans-Sasakian manifolds with a harmonic contact form) and an exhaustive description of the manifolds of this class is obtained. Also, examples of harmonic nearly trans-Sasakian manifolds are given.

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Some Optimal Inequalities for Anti-invariant Submanifolds of the Unit Sphere

Xing,

Yin

2023

J Geom Anal

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Minimal Legendrian submanifolds in Sasakian space forms with C-parallel second fundamental form

Cited by 4 publications

References 27 publications

Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms

Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms

Geometry of Harmonic Nearly Trans-Sasakian Manifolds

Some Optimal Inequalities for Anti-invariant Submanifolds of the Unit Sphere

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