A HOPF THEOREM FOR AMBIENT SPACES OF DIMENSIONS HIGHER THAN THREE

作者：Alencar Hilario^*; do Carmo Manfredo; Tribuzy Renato

来源：Journal of Differential Geometry, 2010, 84(1): 1-17.

We consider surfaces M(2) immersed in E(c)(n) X R, where E(c)(n) is a simply connected n-dimensional complete Riemannian manifold with constant sectional curvature c not equal 0, and assume that the mean curvature vector of the immersion is parallel in the normal bundle. We consider further a Hopf-type complex quadratic form Q on M(2), where the complex structure of M(2) is compatible with the induced metric. It is not hard to check that Q is holomorphic (see [3], p.289).

• 出版日期2010-1