Mayuko Kon

PINCHING THEOREMS FOR A COMPACT MINIMAL SUBMANIFOLD IN A COMPLEX PROJECTIVE SPACE

We give a formula for the Laplacian of the second fundamental form of an n -dimensional compact minimal submanifold M in a complex projective space CP m . As an application of this formula, we prove that M is a geodesic minimal hypersphere in CP m if the sectional curvature satisfies K ≥1/ n , if the normal connection is flat, and if M satisfies an additional condition which is automatically satisfied when M is a CR submanifold. We also prove that M is the complex projective space CP n /2 if K ≥3/ n , and if the normal connection of M is semi-flat.

A characterization of pseudo-Einstein real hypersurfaces of a complex space form

Abstract. We give a characterization of pseudo-Einstein real hypersurfaces of a complex space form. We prove that if the Ricci tensor S of a real hypersurface M of a complex space form with constant principal curvatures satisfies for any , where a is a function and T0 is the holomorphic distribution on M, then M is a pseudo-Einstein real hypersurface.

3-Dimensional Real Hypersurfaces with \(\eta \)-Harmonic Curvature

We classify real hypersurfaces with \(\eta \)-harmonic curvature of a non-flat complex space form of complex dimension 2 under the condition that the Ricci tensor S satisfies \(S\xi =\beta \xi \) where \(\beta \) is a function and \(\xi \) is the structure vector field.

On the Ricci tensor and the generalized Tanaka-Webster connection of real hypersurfaces in a complex space form

We prove that the Ricci tensor Ŝ with respect to the generalized Tanaka-Webster connection of a real hypersurface with the almost contact structure (η, φ, ξ, g) in a complex space form of complex dimension n ≥ 3 satisfies Ŝ(X,φY ) = λg(X,φY ) for any vector field X and Y , λ being a function, if and only if the real hypersurface is locally congruent to some type (A) hypersurface.

A MINIMAL REAL HYPERSURFACE OF A COMPLEX PROJECTIVE SPACE WITH NONNEGATIVE SECTIONAL CURVATURE

We give a characterization of a minimal real hypersurface with respect to the condition for the sectional curvature.