- Volume 47 Issue 6
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CHARACTERIZATIONS OF SOME ISOMETRIC IMMERSIONS IN TERMS OF CERTAIN FRENET CURVES
- Choi, Jin-Ho (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES KYUNGPOOK NATIONAL UNIVERSITY) ;
- Kim, Young-Ho (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES KYUNGPOOK NATIONAL UNIVERSITY) ;
- Tanabe, Hiromasa (YONAGO HIGASHI HIGHSCHOOL)
- Received : 2009.05.07
- Published : 2010.11.30
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.
Supported by : KOSEF
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