Article

# Surfaces with Parallel Mean Curvature Vector in S^2xS^2 and H^2xH^2

08/2008;
Source: arXiv

ABSTRACT Two holomorphic Hopf differentials for surfaces of non-null parallel mean curvature vector in S^2xS^2 and H^2xH^2 are constructed. Using that, we classify those surfaces with vanishing Hopf differentials, and in particular spheres with parallel mean curvature vector.

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### Keywords

holomorphic Hopf differentials

non-null parallel

surfaces

vanishing Hopf differentials