A characterization of totally <Emphasis Type="Italic">η</Emphasis>-umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form |
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Authors: | Mayuko Kon |
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Institution: | (1) Department of Mathematics, Hokkaido University, Kita 10 Nishi 8, Sapporo 060-0810, Japan |
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Abstract: | We give a characterization of totally η-umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition
for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator A of a real hypersurface M of a complex space form M
n
(c), c ≠ 0, n ⩾ 3, satisfies g(AX, Y) = ag(X, Y) for any X, Y ∈ T
0(x), a being a function, where T
0 is the holomorphic distribution on M, then M is a totally η-umbilical real hypersurface or locally congruent to a ruled real hypersurface. This condition for the shape operator is a
generalization of the notion of η-umbilical real hypersurfaces. |
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Keywords: | real hypersurface totally η -umbilical real hypersurface ruled real hypersurface |
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