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2 results

  • Naturally reductive homogeneous real hypersurfaces in quaternionic space forms

  • Part of
  • Setsuo Nagai
  • Journal:
    Journal of the Australian Mathematical Society / Volume 74 / Issue 1 / February 2003
    Published online by Cambridge University Press:
    09 April 2009, pp. 87-100
    Print publication:
    February 2003
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  • We determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space HPn(n ≥ 3). We conclude that the naturally reductive curvature-adapted real hypersurfaces in HPn are Q-quasiumbilical and vice-versa. Further, we study the same problem in quaternionic hyperbolic space HHn(n ≥ 3).

  • Submanifolds with Nonparallel First Normal Bundle

  • Marcos Dajczer, Ruy Tojeiro
  • Journal:
    Canadian Mathematical Bulletin / Volume 37 / Issue 3 / 01 September 1994
    Published online by Cambridge University Press:
    20 November 2018, pp. 330-337
    Print publication:
    01 September 1994
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  • We provide a complete local geometric description of submanifolds of spaces with constant sectional curvature where the first normal spaces, that is, the subspaces spanned by the second fundamental form, form a vector subbundle of the normal bundle of low rank which is nonparallel in the normal connection. We also characterize flat submanifolds with flat normal bundle in Euclidean space satisfying the helix property.