Surfaces with Mean Curvature Vector Parallel in the Normal Bundle

Author:

Chen Bang-Yen,Ludden Gerald D.

Abstract

Let M be a connected surface immersed in a Euclidean m-space Em. Let h be the second fundamental form of this immersion it is a certain symmetric bilinear mapping for X ∈ M, where Tx is the tangent space and the normal space of M at x. Let H be the mean curvature vector of M in Em. If there exists a real λ such that for all tangent vectors X, Y in Tx, then ilf is said to be pseudo-umbilical at x.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. Rigidity theorems for surfaces in euclidean space

2. Isometric Immersions of Constant Mean Curvature and Triviality of the Normal Connection

3. Itoh T. , Minimal surfaces in 4-dimensional Riemannian manifolds of constant curvature, (to appear).

4. Chen B.-Y. , Pseudo-umbilical submanifolds of a Riemannian manifold of constant curvature, III, J. Differential Geometry (to appear).

5. On the mean curvature of submanifolds of euclidean space

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