• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.471-482
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• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.163-176
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• 2016

The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

• 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.