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http://dx.doi.org/10.4134/BKMS.2010.47.6.1285

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.6, 2010 , pp. 1285-1296 More about this Journal
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.
Keywords
Frenet curves of proper order 2; extrinsic spheres; totally geodesic submanifolds; constant isotropic immersions; Veronese embeddings;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
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