Bull. Korean Math. Soc. 2010; 47(6): 1285-1296
Printed November 1, 2010
https://doi.org/10.4134/BKMS.2010.47.6.1285
Copyright © The Korean Mathematical Society.
Jin Ho Choi, Young Ho Kim, and Hiromasa Tanabe
Kyungpook National University, Kyungpook National University, Yonago Higashi Highschool
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.
Keywords: Frenet curves of proper order 2, extrinsic spheres, totally geodesic submanifolds, constant isotropic immersions, Veronese embeddings
MSC numbers: Primary 53B25; Secondary 53C40
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