CHARACTERIZATIONS OF SOME ISOMETRIC IMMERSIONS IN TERMS OF CERTAIN FRENET CURVES
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초록
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.
Abstract
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.
참고문헌 (8)
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