Showing papers by "Young Jin Suh published in 1995"

Characterizations of real hypersurfaces in complex space forms in terms of weingarten map

Abstract: This paper consists of two parts. One is to give the notion of the ruled real hypersurfaces in a complex space form $M_{n}(c),$ $c eq 0$ and to calculate the expression of the covariant derivative of its Weingarten map. Moreover, we know that real hypersurfaces of type $A$ also satisfy this expression. The other is to show that ruled real hypersurfaces or real hypersurfaces of type $A$ are the only real hypersurfaces in $M_{n}(c)$ which satisfy this expression.

Characterizations of real hypersurfaces in complex space forms in terms of curvature tensors

Abstract: A complex n-dimensional Kahler 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=Q or c<0. In this study of real hypersurfaces of PnC, Takagi [8] classifiedall homogeneous real hypersurfaces and Cecil and Ryan [2] showed also that they are realized as the tubes of constant radius over Kahler submanifolds if the structure vector field$ is principal. And Berndt [1] classifiedall homogeneous real hypersurfaces of HnC and showed that they are realized as the tubes of constant radius over certain submanifolds. According to Takagi's classification theorem and Berndt's one, the principal curvatures and their multiplicitiesof homogeneous real hypersurfaces of Mn(c) are given. Now, let M be a real hypersurface of Mn(c), c^O. Then M has an almost contact metric structure (0, ?, 7],g) induced from the Kahler metric and the almost complex structure of Mn(c). We denote by A the shape operator in the direction of the unit normal on M. Then Okumura [7] and Montiel and Romerc ffilnrnvpri the fnilnwincr

Characterizations of some real hypersurfaces in a complex space form in terms of lie derivative

Abstract: A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c