Bang-Yen Chen

Total mean curvature and submanifolds of finite type

Differentiable Manifolds Riemannian and Pseudo-Riemannian Manifolds Hodge Theory and Spectral Geometry Submanifolds Total Mean Curvature Submanifolds of Finite Type Biharmonic Submanifolds and Biharmonic Conjectures lambda-biharmonic and Null 2-type Submanifolds Applications of Finite Type Theory Additional Topics in Finite Type Theory

On totally real submanifolds

Complex analytic submanifolds and totally real submanifolds are two typical classes among all submanifolds of an almost Hermitian mani- fold. In this paper, some characterizations of totally real submanifolds are given. Moreover some classifications of totally real submanifolds in complex space forms are obtained.

Totally geodesic submanifolds of symmetric spaces, I

One purpose of this article is to establish a general method to determine stability of totally geodesic submanifolds of symmetric spaces. The method is used to determine the stability of the basic totally geodesic submanifolds M+,M introduced and studied by Chen and Nagano in (Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45 (1978), 405-425) as minimal submanifolds. The other purpose is to establish a stability theorem for minimal totally real sub- manifolds of Kahlerian manifolds.

Pseudo-riemannian geometry, δ-invariants and applications

Pseudo-Riemannian Manifolds Pseudo-Riemannian Submanifolds Warped Products and Twisted Products Robertson-Walker Spacetimes Hodge Theory and Elliptic Differential Operators Submanifolds of Finite Type Total Mean Curvature δ-Invariants, Inequalities Submanifolds of Kaehler Manifolds Submanifolds of Para-Kaehler Manifolds Pseudo-Riemannian Submersions Affine Hypersurface Contact Geometry Applications of δ-Invariants Applications to Relativity.

Geometry of Warped Product CR-Submanifolds in Kaehler Manifolds

Abstract. A CR-submanifold N of a Kaehler manifold is called a CR-warped product if N is the warped product of a holomorphic submanifold and a totally real submanifold of . This notion of CR-warped products was introduced in part I of this series. It was proved in part I that every CR-warped product in a Kaehler manifold satisfies a basic inequality: . The classification of CR-warped products in complex Euclidean space satisfying the equality case of the inequality is archived in part I. The main purpose of this second part of this series is to classify CR-warped products in complex projective and complex hyperbolic spaces which satisfy the equality.

Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions

First we define the notion of k-Ricci curvature of a Riemannian n- manifold. Then we establish sharp relations between the k-Ricci curvature and the shape operator and also between the k-Ricci curvature and the squared mean cur- vature for a submanifold in a Riemannian space form with arbitrary codimension. Several applications of such relationships are also presented.

When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane

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On CR-submanifolds of Hermitian manifolds

In this paper we consider a CR-submanifold of a Hermitian manifold and prove various integrability theorems on the submanifold. When the ambient space is Kaehlerian a number of differential geometric results are also obtained.

ON ISOMETRIC MINIMAL IMMERSIONS FROM WARPED PRODUCTS INTO REAL SPACE FORMS

We establish a general sharp inequality for warped products in real space form. As applications, we show that if the warping function

INTERACTION OF LEGENDRE CURVES AND LAGRANGIAN SUBMANIFOLDS

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