DOI QR코드

DOI QR Code

CHARACTERIZATIONS OF SOME ISOMETRIC IMMERSIONS IN TERMS OF CERTAIN FRENET CURVES

  • Choi, Jin-Ho ;
  • Kim, Young-Ho ;
  • Tanabe, Hiromasa
  • Received : 2009.05.07
  • Published : 2010.11.30

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

References

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Acknowledgement

Supported by : KOSEF