Surfaces with Mean Curvature Vector Parallel in the Normal Bundle

Abstract

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