• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.432-439
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• 1998

The main purpose of this paper is to give a characterization of a totally geodesic Kaehler submanifold M of a Kaehler manifold $\tilde{M}$ by observing the extrinsic shape of particular circles of the submanifold M.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.253-264
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• 2017

We first extend Yano-Nomizu's theorem, which characterizes extrinsic spheres in a Riemannian manifold, for Riemannian maps. Then we introduce Clairaut Riemannian maps, give an example and obtain necessary and sufficient conditions for a Riemannian map to be Clairaut type.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1285-1296
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• 2010

We give criterions for a submanifold to be an extrinsic sphere and to be a totally geodesic submanifold by observing some Frenet curves of order 2 on the submanifold. We also characterize constant isotropic immersions into arbitrary Riemannian manifolds in terms of Frenet curves of proper order 2 on submanifolds. As an application we obtain a characterization of Veronese embeddings of complex projective spaces into complex projective spaces.