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Quasi-conformally flat submanifolds with parallel mean curvature vector

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2 Author(s)
He, Hulxla ; Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China ; Liu, Fang

This paper studied the conditions such that an n-dimensional complete space-like submanifold M with a parallel mean curvature vector field in an indefinite space form Sn+p (c)(p ≥ 2, n≥ 3) is a totally umbilical submanifold. By means of Laplacian estimation and the choice of a diagonal frame field, the following theorem is proved: if Mis quasi-conformally flat and H2≤ c, Ric $(M) leq delta_{M} < [(n-1)-(1)/(t)](c-H^{2})$, then M is a totally umbilical submanifold.

Published in:

Tsinghua Science and Technology  (Volume:9 ,  Issue: 1 )