• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.215-236
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• 1994

The purpose of the present paper is to study generic submanifolds of a Sasakian space form with nonvanishing parallel mean curvature vector field such that the shape operator in the direction of the mean curvature vector field commutes with the structure tensor field induced on the submanifold. In .cint. 1 we state general formulas on generic submanifolds of a Sasakian manifold, especially those of a Sasakian space form. .cint.2 is devoted to the study a generic submanifold of a Sasakian manifold, which is not tangent to the structure vector. In .cint.3 we investigate generic submanifolds, not tangent to the structure vector, of a Sasakian space form with nonvanishing parallel mean curvature vactor field. In .cint.4 we discuss generic submanifolds tangent to the structure vector of a Sasakian space form and compute the restricted Laplacian for the shape operator in the direction of the mean curvature vector field. As a applications of these, in the last .cint.5 we prove our main results.

• East Asian mathematical journal
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• v.24 no.4
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• pp.415-419
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• 2008

Let M be a generic submanifold of $S^n\;{\times}\;S^n$. If M admits an Sasakian structure, then M is a Brieskorn manifold.

• 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.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.985-994
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• 2021

The object of this paper is to study non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds equipped with (f, g, u, v, λ)-structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non-invariant hypersurface with (f, g, u, v, λ)-structure of a (𝜖, 𝛿)-trans Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds with (f, g, u, v, λ)-structure has been traced under the condition when f is parallel.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.341-358
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• 2023

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖T^k × M^2n+1-k or gradient 𝜂-Yamabe soliton.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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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.

• 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.

• 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.

• 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.

• 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).