Showing papers in "Communications of The Korean Mathematical Society in 1992"

On certain real hypersurfaces of a complex space form

Abstract: A complex n-diemensional Kaehler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by Mn(c) A complete and simply connected complex space form consists of a complex projective space PnC , a complex Euclidean space Cn or a complex hyperbolic space HnC , according as c > 0, c = 0 or c < 0 Let M be a real hypersurface of Mn(c), c 6= 0 Then M has an almost contact metric structure (φ, ξ, η, g) induced from the Kaehler metric and the almost complex structure J of Mn(c) We denote by A and S the shape operator and the Ricci tensor of type (1,1) on M , respectively On his study of real hypersurfaces of a complex projective space PnC , Takagi [7] classified all homogeneous real hypersurfaces and showed that they are realized as the tubes of constant radius over Kaehler submanifolds if ξ is principal Namely, he proved the following