• 제목/요약/키워드: ${\alpha}$-Sasakian

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On Lorentzian α-Sasakian Manifolds

  • Yildiz, Ahmet;Murathan, Cengizhan
    • Kyungpook Mathematical Journal
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    • 제45권1호
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    • pp.95-103
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    • 2005
  • The present paper deals with Lorentzian ${\alpha}-Sasakian$ manifolds with conformally flat and quasi conform ally flat curvature tensor. It is shown that in both cases, the manifold is locally isometric with a sphere $S^{2^{n}+1}(c)$. Further it is shown that an Lorentzian ${\alpha}-Sasakian$ manifold with R(X, Y).C = 0 is locally isometric with a sphere $S^{2^{n}+1}(c)$, where c = ${\alpha}^2$.

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

  • De, Uday Chand;Arslan, Kadri
    • 대한수학회보
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    • 제46권3호
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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.

ON GENERALIZED RICCI-RECURRENT TRANS-SASAKIAN MANIFOLDS

  • Kim, Jeong-Sik;Prasad, Rajendra;Tripathi, Mukut-Mani
    • 대한수학회지
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    • 제39권6호
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    • pp.953-961
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    • 2002
  • Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.

A Class of Lorentzian α-Sasakian Manifolds

  • Yildiz, Ahmet;Turan, Mine;Murathan, Cengizhan
    • Kyungpook Mathematical Journal
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    • 제49권4호
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    • pp.789-799
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    • 2009
  • In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.

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

  • Kazan, Ahmet;Karadag, H.Bayram
    • 호남수학학술지
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    • 제40권3호
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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.

INDEFINITE TRANS-SASAKIAN MANIFOLD ADMITTING AN ASCREEN HALF LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • 대한수학회논문집
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    • 제29권3호
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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.

INVARIANT NULL RIGGED HYPERSURFACES OF INDEFINITE NEARLY α-SASAKIAN MANIFOLDS

  • Mohamed H. A. Hamed;Fortune Massamba
    • 대한수학회논문집
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    • 제39권2호
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    • pp.493-511
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    • 2024
  • We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly α-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly α-Sasakian structures.

LOXODROMES AND TRANSFORMATIONS IN PSEUDO-HERMITIAN GEOMETRY

  • Lee, Ji-Eun
    • 대한수학회논문집
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    • 제36권4호
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    • pp.817-827
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    • 2021
  • In this paper, we prove that a diffeomorphism f on a normal almost contact 3-manifold M is a CRL-transformation if and only if M is an α-Sasakian manifold. Moreover, we show that a CR-loxodrome in an α-Sasakian 3-manifold is a pseudo-Hermitian magnetic curve with a strength $q={\tilde{r}}{\eta}({\gamma}^{\prime})=(r+{\alpha}-t){\eta}({\gamma}^{\prime})$ for constant 𝜂(𝛄'). A non-geodesic CR-loxodrome is a non-Legendre slant helix. Next, we prove that let M be an α-Sasakian 3-manifold such that (∇YS)X = 0 for vector fields Y to be orthogonal to ξ, then the Ricci tensor 𝜌 satisfies 𝜌 = 2α2g. Moreover, using the CRL-transformation $\tilde{\nabla}^t$ we fine the pseudo-Hermitian curvature $\tilde{R}$, the pseudo-Ricci tensor $\tilde{\rho}$ and the torsion tensor field $\tilde{T}^t(\tilde{S}X,Y)$.