• Honam Mathematical Journal
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• v.26 no.2
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• pp.155-161
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• 2004

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.55-65
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• 2005

We find the expression of the curvature tensor field for a manifold with is endowed with an almost contact structure satisfying the condition (1.7). By using this condition we obtain some properties of the Ricci tensor and scalar curvature (d. Theorem 3.2 and Proposition 3.2).

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.179-191
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• 2022

We set our target to investigate Yamabe solitons, gradient Yamabe solitons and gradient Einstein solitons within the structure of 3-dimensional non-cosymplectic normal almost contact metric manifolds. Also, we provide a nontrivial example and validate a result of our paper.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.805-812
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• 2014

For unit tangent sphere bundles $T_1M$ with the standard contact metric structure (${\eta},\bar{g},{\phi},{\xi}$), we have two fundamental operators that is, $h=\frac{1}{2}{\pounds}_{\xi}{\phi}$ and ${\ell}=\bar{R}({\cdot},{\xi}){\xi}$, where ${\pounds}_{\xi}$ denotes Lie differentiation for the Reeb vector field ${\xi}$ and $\bar{R}$ denotes the Riemmannian curvature tensor of $T_1M$. In this paper, we study the Reeb ow invariancy of the corresponding (0, 2)-tensor fields H and L of h and ${\ell}$, respectively.

• East Asian mathematical journal
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• v.16 no.2
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• pp.383-390
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• 2000

This paper is to show that a submanifold of codimension 2 of an odd-dimensional sphere with an almost contact metric structure is an intersection of a complex cone with generator as a normal vector and a sphere.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1255-1265
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• 2009

We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M, g) of constant radius $\gamma$ reduces essentially to the one of unit tangent sphere bundle of a Riemannian manifold equipped with the respective induced Sasaki metrics. Further, we provide some applications of this theorem on the $\eta$-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.573-589
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• 2006

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ in a non flat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is ${\xi}$-parallel and the Ricci tensor S commutes with the structure operator $\phi$, then a real hypersurface in $M_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_n(c)$.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.321-335
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• 2006

Generic submanifolds of a Riemannian manifold endowed with a hypercosymplectic 3-structure are studied. Integrability conditions for certain distributions on the generic submanifold are discussed. Geometry of leaves of certain distributions are also studied.

• East Asian mathematical journal
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• v.37 no.1
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• pp.97-107
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• 2021

Let M be a real hypersurface with almost contact metric structure (��, ξ, ��, g) in a nonflat complex space form Mn(c). We denote S and Rξ by the Ricci tensor of M and by the structure Jacobi operator with respect to the vector field ξ respectively. In this paper, we prove that M is a Hopf hypersurface of type (A) in Mn(c) if it satisfies Rξ�� = ��Rξ and at the same time satisfies $({\nabla}_{{\phi}{\nabla}_{\xi}{\xi}}R_{\xi}){\xi}=0$ or Rξ��S = S��Rξ.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.609-617
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• 2019

We characterize two-point homogeneous spaces M by means of the structural operator $h={\frac{1}{2}}{\mathcal{L}}_{\xi}{\phi}$ or the characteristic Jacobi operator ${\ell}=R({\cdot},{\xi}){\xi}$ on the unit tangent sphere bundles $T_1M$.