• Title/Summary/Keyword: trans-Sasakian manifold

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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.

INDEFINITE TRANS-SASAKIAN MANIFOLD WITH A TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • East Asian mathematical journal
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    • v.33 no.5
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    • pp.533-542
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    • 2017
  • We study the geometry of indefinite trans-Sasakian manifold ${\bar{M}}$ admitting a half lightlike submanifold M such that the structure vector field of ${\bar{M}}$ belongs to the transversal vector bundle of M. We prove several classification theorems of such an indefinite trans-Sasakian manifold.

TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO GENERALIZED TANAKA-WEBSTER CONNECTION

  • Kazan, Ahmet;Karadag, H.Bayram
    • Honam Mathematical Journal
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    • v.40 no.3
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    • pp.487-508
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    • 2018
  • In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (${\alpha},{\beta}$) and obtain the curvature tensors of a trans-Sasakian manifold with respect to this connection. Also, we investigate some special curvature conditions of a trans-Sasakian manifold with respect to generalized Tanaka-Webster connection and finally, give an example for trans-Sasakian manifolds.

ON A CLASS OF THREE-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS

  • De, Uday Chand;De, Krishnendu
    • Communications of the Korean Mathematical Society
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    • v.27 no.4
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    • pp.795-808
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    • 2012
  • The object of the present paper is to study 3-dimensional trans-Sasakian manifolds with conservative curvature tensor and also 3-dimensional conformally flat trans-Sasakian manifolds. Next we consider compact connected $\eta$-Einstein 3-dimensional trans-Sasakian manifolds. Finally, an example of a 3-dimensional trans-Sasakian manifold is given, which verifies our results.

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.

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.

3-Dimensional Trans-Sasakian Manifolds with Gradient Generalized Quasi-Yamabe and Quasi-Yamabe Metrics

  • Siddiqi, Mohammed Danish;Chaubey, Sudhakar Kumar;Ramandi, Ghodratallah Fasihi
    • Kyungpook Mathematical Journal
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    • v.61 no.3
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    • pp.645-660
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    • 2021
  • This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.

ON PSEUDO-SLANT SUBMANIFOLDS OF A NEARLY (ε, δ)-TRANS SASAKIAN MANIFOLD

  • Jun, Jae-Bok;Rahman, Shamsur
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.935-949
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    • 2019
  • The purpose of the paper is to study the notion of pseudo-slant submanifolds and the existence of some structures on a pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold. Totally umbilical proper-slant submanifolds are worked out. We discuss the integrability of distributions on pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold.