• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.133-141
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• 2009

We study on semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds. We prove that a (2n + 1)-dimensional Sasakian hypersurface M of a (2n+2)-dimensional Kaehler manifold $\widetilde{M}^{2n+2}$ is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and $\widetilde{M}^4$ is a Calabi-Yau manifold, then $\widetilde{M}$ is flat at each point of M. We also prove that such a hypersurface M is Weyl-semiparallel if and only if it is either an ${\eta}$-Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• 대한수학회논문집
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• 제36권2호
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• pp.377-387
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• 2021

In the present paper, we characterize quasi-Sasakian 3-manifolds admitting 𝜂-Ricci solitons. Finally, the existence of 𝜂-Ricci soliton in a quasi-Sasakian 3-manifold has been proved by a concrete example.

• 대한수학회보
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• 제59권1호
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• pp.101-110
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• 2022

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.

• 대한수학회논문집
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• 제35권2호
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• pp.625-637
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• 2020

The object of the present paper is to characterize 3-dimensional trans-Sasakian manifolds of type (α, β) admitting ∗-Ricci solitons and ∗-gradient Ricci solitons. Under certain restrictions on the smooth functions α and β, we have proved that a trans-Sasakian 3-manifold of type (α, β) admitting a ∗-Ricci soliton reduces to a β-Kenmotsu manifold and admitting a ∗-gradient Ricci soliton is either flat or ∗-Einstein or it becomes a β-Kenmotsu manifold. Also an illustrative example is presented to verify our results.

• 대한수학회논문집
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• 제34권3호
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• pp.881-896
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• 2019

In the present paper, we study certain curvature conditions satisfying by the projective curvature tensor in Sasakian manifolds with respect to the generalized-Tanaka-Webster connection. Finally, we give an example of a 3-dimensional Sasakian manifold with respect to the generalized-Tanaka-Webster connection.

• 대한수학회보
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• 제33권2호
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• pp.243-251
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• 1996

In a Sasakian manifold, a C-Bochner curvature tensor is constructed from the Bochner curvature tensor in a Kaehlefian manifold by the fibering of Boothby-wang[2]. Many subjects for vanishing C-Bocher curvature tensor with constant scalar curvature were studied in [3], [6], [7], [9], [10], [11] and so on.

• 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 $\tilde{T}^t(\tilde{S}X,Y)$.

• 대한수학회논문집
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• 제34권2호
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• pp.615-632
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• 2019

We study generic lightlike submanifolds M of an indefinite trans-Sasakian manifold ${\bar{M}}$ or an indefinite generalized Sasakian space form ${\bar{M}}(f_1,f_2,f_3)$ endowed with an $({\ell},m)$-type metric connection subject such that the structure vector field ${\zeta}$ of ${\bar{M}}$ is tangent to M.

• 대한수학회논문집
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• 제35권4호
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• pp.1269-1281
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• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.