• Title/Summary/Keyword: Sasakian

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h-almost Ricci Solitons on Generalized Sasakian-space-forms

  • Doddabhadrappla Gowda, Prakasha;Amruthalakshmi Malleshrao, Ravindranatha;Sudhakar Kumar, Chaubey;Pundikala, Veeresha;Young Jin, Suh
    • Kyungpook Mathematical Journal
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    • v.62 no.4
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    • pp.715-728
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    • 2022
  • The aim of this article is to study the h-almost Ricci solitons and h-almost gradient Ricci solitons on generalized Sasakian-space-forms. First, we consider h-almost Ricci soliton with the potential vector field V as a contact vector field on generalized Sasakian-space-form of dimension greater than three. Next, we study h-almost gradient Ricci solitons on a three-dimensional quasi-Sasakian generalized Sasakian-space-form. In both the cases, several interesting results are obtained.

INDEFINITE TRANS-SASAKIAN MANIFOLD ADMITTING AN ASCREEN HALF LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.29 no.3
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    • pp.451-461
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    • 2014
  • We study the geometry of indefinite trans-Sasakian manifold $\bar{M}$, of type (${\alpha},{\beta}$), admitting a half lightlike submanifold M such that the structure vector field of $\bar{M}$ does not belong to the screen and coscreen distributions of M. The purpose of this paper is to prove several classification theorems of such an indefinite trans-Sasakian manifold.

CERTAIN CURVATURE CONDITIONS ON AN LP-SASAKIAN MANIFOLD WITH A COEFFICIENT α

  • De, Uday Chand;Arslan, Kadri
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.401-408
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    • 2009
  • The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient $\alpha$. Among others it is shown that if an LP-Sasakian manifold with a coefficient $\alpha$ is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient $\alpha$ is a spaceform.

INDEFINITE GENERALIZED SASAKIAN SPACE FORM ADMITTING A GENERIC LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1711-1726
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    • 2014
  • In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

Indefinite Generalized Sasakian Space Form Admitting a Lightlike Hypersurface

  • JIN, DAE HO
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.1097-1104
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    • 2015
  • In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a lightlike hypersurface M subject such that the almost contact structure vector field ${\zeta}$ of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. We prove a classification theorem of such an indefinite generalized Sasakian space form.

MINIMAL AND HARMONIC REEB VECTOR FIELDS ON TRANS-SASAKIAN 3-MANIFOLDS

  • Wang, Yaning
    • Journal of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1321-1336
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    • 2018
  • In this paper, we obtain some necessary and sufficient conditions for the Reeb vector field of a trans-Sasakian 3-manifold to be minimal or harmonic. We construct some examples to illustrate main results. As applications of the above results, we obtain some new characteristic conditions under which a compact trans-Sasakian 3-manifold is homothetic to either a Sasakian or cosymplectic 3-manifold.

SOME RECURRENT PROPERTIES OF LP-SASAKIAN NANIFOLDS

  • Venkatesha, Venkatesha;Somashekhara., P.
    • Korean Journal of Mathematics
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    • v.27 no.3
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    • pp.793-801
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    • 2019
  • The aim of the present paper is to study certain recurrent properties of LP-Sasakian manifolds. Here we first describe Ricci ${\eta}$-recurrent LP-Sasakian manifolds. Further we study semi-generalized recurrent and three dimensional locally generalized concircularly ${\phi}$-recurrent LP-Sasakian manifolds and got interesting results.

ON 3-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO SEMI-SYMMETRIC METRIC CONNECTION

  • Pahan, Sampa
    • Journal of the Chungcheong Mathematical Society
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    • v.34 no.3
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    • pp.235-251
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    • 2021
  • The aim of the present paper is to study 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Firstly, we prove that extended generalized M-projective 𝜙-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection is an 𝜂-Einstein manifold with respect to Levi-Civita connection under some certain conditions. Later we study some curvature properties of 3-dimensional trans-Sasakian manifold admitting the above connection.

THE FIRST POSITIVE AND NEGATIVE DIRAC EIGENVALUES ON SASAKIAN MANIFOLDS

  • Eui Chul Kim
    • Journal of the Korean Mathematical Society
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    • v.60 no.5
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    • pp.999-1021
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    • 2023
  • Using the results in the paper [12], we give an estimate for the first positive and negative Dirac eigenvalue on a 7-dimensional Sasakian spin manifold. The limiting case of this estimate can be attained if the manifold under consideration admits a Sasakian Killing spinor. By imposing the eta-Einstein condition on Sasakian manifolds of higher dimensions 2m + 1 ≥ 9, we derive some new Dirac eigenvalue inequalities that improve the recent results in [12, 13].

THE STUDY OF *-RICCI TENSOR ON LORENTZIAN PARA SASAKIAN MANIFOLDS

  • M. R. Bakshi;T. Barman;K. K. Baishya
    • Honam Mathematical Journal
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    • v.46 no.1
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    • pp.70-81
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    • 2024
  • We consider the *-general critical equation on LP Sasakian manifolds, and show that such a manifold is generalized η-Einstein. After then, we consider LP Sasakian manifolds with *-conformally semisymmetric condition, and show that such manifolds are *-Einstein. Moreover, we show that the *-conformally semisymmetric LP Sasakian manifold is locally isometric to En+1(0) × Sn(4).