• 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.38 no.2
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• pp.375-384
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• 2016

In this paper, we study the pseudo-symmetry of unit tangent sphere bundle. We prove that if the unit tangent sphere bundle $T_1M$ with standard contact metric structure over a locally symmetric $M^n$, $n{\geq}3$ is pseudo-symmetric, then M is of constant curvature.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.329-340
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• 2011

We shall give some curvature conditions for the unit tangent sphere bundle of an n($\geq$ 4)-dimensional Riemannian manifold to be H-contact. Furthermore, we provide an example illustrating Main Theorem.

• 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 $T_1M$.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.811-819
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• 2020

We give characterizations of locally symmetric spaces M via the structural operator $h={\frac{1}{2}{\mathcal{L}}_{\xi}{\phi}}$ or the characteristic Jacobi operator ℓ = R(·, ξ)ξ on the unit tangent sphere bundles T1M.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1715-1723
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• 2016

We study the characteristic Jacobi operator ${\ell}={\bar{R}({\cdot},{\xi}){\xi}$ (along the Reeb flow ${\xi}$) on the unit tangent sphere bundle $T_1M$ over a Riemannian manifold ($M^n$, g). We prove that if ${\ell}$ is pseudo-parallel, i.e., ${\bar{R}{\cdot}{\ell}=L{\mathcal{Q}}({\bar{g}},{\ell})$, by a non-positive function L, then M is locally flat. Moreover, when L is a constant and $n{\neq}16$, M is of constant curvature 0 or 1.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1035-1047
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• 2004

In this paper, we study the unit tangent sphere bundles T$_1$M(4c) of complex space forms M(4c) with constant holomorphic sectional curvature 4c. In particular, we determine T$_1$M(4c) whose Ricci tensors satisfy the Einstein-like conditions.

• 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.