J. Aust. Math. Soc.  74 (2003), 87-99
Naturally reductive homogeneous real hypersurfaces in quaternionic space forms

Setsuo Nagai
  Department of Mathematics
  Faculty of Education
  Toyama University
  3190 Gofuku
  Toyamashi 930-8555
  Japan
  snagai@edu.toyama-u.ac.jp


Abstract
We determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space $\mathbb{H}P^n$ ($n\geq 3$). We conclude that the naturally reductive curvature-adapted real hypersurfaces in $\mathbb{H}P^n$ are Q-quasiumbilical and vice-versa. Further, we study the same problem in quaternionic hyperbolic space $\mathbb{H}H^n$ ($n\geq 3$).
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