• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.135-142
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• 2013

In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.347-354
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• 2018

Let ${\mathcal{C}}$, ${\mathcal{M}}$, ${\mathcal{L}}$ be concircular curvature tensor, M-projective curvature tensor and conharmonic curvature tensor, respectively. We obtain that if a non-Kenmotsu ($k,{\mu}$)'-almost Kenmotsu manifold satisfies ${\mathcal{C}}{\cdot}{\mathcal{S}}=0$, ${\mathcal{R}}{\cdot}{\mathcal{M}}=0$ or ${\mathcal{R}}{\cdot}{\mathcal{L}}=0$, then it is locally isometric to the Riemannian product ${\mathds{H}}^{n+1}(-4){\times}{\mathds{R}}^n$.