- Volume 47 Issue 6
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.
Frenet curves of proper order 2;extrinsic spheres;totally geodesic submanifolds;constant isotropic immersions;Veronese embeddings
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Supported by : KOSEF