• Title/Summary/Keyword: constant isotropic immersions

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CHARACTERIZATIONS OF SOME ISOMETRIC IMMERSIONS IN TERMS OF CERTAIN FRENET CURVES

  • Choi, Jin-Ho;Kim, Young-Ho;Tanabe, Hiromasa
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1285-1296
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    • 2010
  • 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.