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- W206140263 abstract "Abstract. The purpose of the present paper is to prove: Let M be aKaehler hypersurface of a complex space form M~ ( c ) of constant holomor-phic sectional curvature c . Then the following conditions are equivalent:(A) M has the recurrent second fundamental form. (B) M has the bire-current second fundamental form. (C) the derivation R ( X;Y ) and thesecond fundamental form are commutative. (D) M is totally geodesic in M~ ( c ).M.S.C. 2000: 53C40, 53B25.Key words: Kaehler hypersurface, the recurrent second fundamental form, totallygeodesic. 1 Introduction Let M~ ( c ) be a complex space form (i.e. a complete, simply-connected Kaehler mani-fold) of the complex dimension n +1 with constant holomorphic sectional curvature c .If c is positive, then M~ ( c ) is the complex projective space P n +1 ( c ) with the Fubini-Study metric of constant holomorphic sectional curvature c . If c is negative, then M~ ( c ) is the complex hyperbolic space D n +1 ( c ) with the Bergman metric of constantholomorphic sectional curvature" @default.
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- W206140263 date "2008-01-01" @default.
- W206140263 modified "2023-09-27" @default.
- W206140263 title "On a Kaehler hypersurface of a complex space form with the recurrent second fundamental form" @default.
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