Real hypersurfaces in complex two-plane Grassmannians related to the Ricci curvature

Young Suh, Yoshiyuki Watanabe
2005 Toyama Math. J   unpublished
In this paper we introduce a new notion of the Ricci tensor derived from the curvature tensor of real hypersurfaces in complex two-plane Grassmannians G 2 (C m+2). Moreover, we give a characterization of real hypersurfaces of type A in G 2 (C m+2), that is, a tube over a totally geodesic G 2 (C m+1) in G 2 (C m+2) in terms of integral formulas related to the Ricci curvature Ric(ξ, ξ) along the direction of the structure vector field ξ for real hypersurfaces in G 2 (C m+2). 0. Introduction In
more » ... geometry of real hypersurfaces in complex space forms or in quaternionic space forms there have been many characterizations of model hypersurfaces of type A 1 , A 2 , B, C, D and E in complex projective space CP m , of type A 0 , A 1 , A 2 and B in complex hyperbolic space CH m or A 1 , A 2 , B in quaternionic projective space QP m , which are completely classified by Cecil and Ryan [4], Kimura [5], Berndt [1], Martinez and Pérez [6] respectively. Among them there were some characterizations of homogeneous real hypersurfaces of type A 1 , A 2 in complex projective space CP m and of type A 0 , A 1 , A 2 in complex hyperbolic space CH m. As an example, we say
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