Song-How Kon

Bio: Song-How Kon is an academic researcher from University of Malaya. The author has contributed to research in topics: Ricci curvature & Scalar curvature. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.

On Hopf hypersurfaces in a non-flat complex space form with η-recurrent Ricci tensor

Abstract: Baikoussis, Lyu and Suh [1] showed that a Hopf hypersurface M in a non-flat complex space form M-n(c) with constant mean curvature and with eta-recurrent Ricci tensor is locally congruent to one of real hypersurfaces of type A and B. They also conjectured that the same result can be obtained even without the constancy assumption on the mean curvature (cf. [I, Remark 5.1.]). The purpose of this paper is to answer this question in the affirmative.

Real Hypersurfaces in Complex Space Forms

Abstract: The study of real hypersurfaces in complex projective space CP n and complex hyperbolic space CH n began at approximately the same time as Munzner’s work on isoparametric hypersurfaces in spheres. A key early work was Takagi’s classification [669] in 1973 of homogeneous real hypersurfaces in CP n . These hypersurfaces necessarily have constant principal curvatures, and they serve as model spaces for many subsequent classification theorems. Later Montiel [501] provided a similar list of standard examples in complex hyperbolic space CH n . In this chapter, we describe these examples of Takagi and Montiel in detail, and later we prove many important classification results involving them. We also study Hopf hypersurfaces, focal sets, parallel hypersurfaces and tubes using both standard techniques of submanifold geometry and the method of Jacobi fields.

Real hypersurfaces of complex space forms satisfying Fischer–Marsden equation

Abstract: Let M be a real hypersurface of a complex space form of constant curvature c. In this paper, we study the hypersurface M which admits a nontrivial solution to Fischer–Marsden equation, that is, the induce metric g of M satisfies $$ Hess _g( u )=(\varDelta _g u )g+ u S_g$$ , where $$ u $$ is a nontrivial function. We prove that there does not exist a complete Hopf real hypersurface in a non-flat complex space form satisfying Fischer–Marsden equation. Finally, we show that a complete real hypersurface with $$A\xi =\alpha \xi $$ , $$\alpha e 0$$ , of a complex Euclidean space $${\mathbb {C}}^n$$ satisfying Fischer–Marsden equation is locally congruent to a sphere or $${\mathbb {S}}^1 \times {\mathbb {R}}^{2n-2}$$ .

On a Class of Real Hypersurfaces in a Complex Space Form with Weakly \phi -Invariant Shape Operator

Abstract: In this paper, we study real hypersurfaces in a complex space form with weakly \(\phi \)-invariant shape operator, where \(\phi \) is the almost contact structure on the real hypersurfaces induced by the complex structure on its ambient space. We first construct a class of real hypersurfaces with weakly \(\phi \)-invariant shape operator in complex Euclidean spaces and complex projective spaces and then give a characterization of such a class of real hypersurfaces. With this results, we classify minimal real hypersurfaces with weakly \(\phi \)-invariant shape operator in complex Euclidean spaces and in complex projective spaces.