Groupes et algébres de lie

Introduction to lie algebras and representation theory

An Introduction to Magnetohydrodynamics

(1.1) Some of the main results described in [Report] are the following (in rough terms; notations and precise references will be given below): (1) A map (f>:{M,g)-+(N,h) between Riemannian manifolds which is continuous and of class L\\ is harmonic if and only if it is a critical point of the energy functional. (2) Let (M, g) and (N, h) be compact, and <̂ 0: (M, g) -> (N, h) a map. Then ^0 can be deformed to a harmonic map with minimum energy in its homotopy class in the following cases: (a) Riem ' f t ^0; (b) dim M = 2 and n2(N) = 0. (3) Any map 0O: S m -> S can be deformed to a harmonic map provided m ^ 7. More generally, suitably restricted harmonic polynomial maps can be joined to provide harmonic maps between spheres. (4) The homotopy class of maps of degree 1 from the 2-torus T to the 2-sphere S has no harmonic representative, whatever Riemannian metrics are put on T and S. (5) If in (2) M has a smooth boundary, then various Dirichlet problems have solutions in case (a) and (b); and also when the boundary data is sufficiently small.

Another Report on Harmonic Maps

Certain conditions for a Riemannian manifold to be isometric with a sphere:Dedicated to Professor Kentaro Yano on his fiftieth birthday

Geometry of submanifolds

By BANG-YEN CHEN 1. Introduction. Let x: M -* E" be an immersion from an n-dimensional (n > 0) mani- fold into a Euclidean re, space. Denote by A the Laplacian operator of M with respect to the induced metric. Then we have the following formula of Beltrami: (1.1)

Some pinching and classification theorems for minimal submanifolds

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

Total Mean Curvature and Submanifolds of Finite Type

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.

https://www.ams.org/tran/1974-193-00/S0002-9947-1974-0346708-7/S0002-9947-1974-0346708-7.pdf

On totally real submanifolds

The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The main purpose of these talks is to present some of author's work and also his joint works with Professor T. Nagano and Professor Y. Tazawa of Japan, Professor P. F. Leung of Singapore and Professor J. M. Morvan of France on geometry of slant submanifolds and its related subjects in a systematical way.

Bang-Yen Chen

Papers

Geometry of submanifolds

Some pinching and classification theorems for minimal submanifolds

Total Mean Curvature and Submanifolds of Finite Type

On totally real submanifolds

Geometry of Slant Submanifolds