A hopf theorem for ambient spaces of dimensions higher than three

Hilário Alencar Instituto de Matem´atica Manfredo do Carmo Estrada D. Castorina Renato Tribuzy Universidade Federal do Amazonas

Differential Geometry mathscidoc:1609.10153

Journal of Differential Geometry, 84, (1), 1-17, 2010
We consider surfaces M2 immersed in En c × R, where En c is a simply connected n-dimensional complete Riemannian manifold with constant sectional curvature c 6= 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 M2, where the complex structure of M2 is compatible with the induced metric. It is not hard to check that Q is holomorphic (see [3], p.289). We will use this fact to give a reasonable description of immersed surfaces in En c ×R that have parallel mean curvature vector.
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@inproceedings{hilário2010a,
  title={A HOPF THEOREM FOR AMBIENT SPACES OF DIMENSIONS HIGHER THAN THREE},
  author={Hilário Alencar, Manfredo do Carmo, and Renato Tribuzy},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911204258077065810},
  booktitle={Journal of Differential Geometry},
  volume={84},
  number={1},
  pages={1-17},
  year={2010},
}
Hilário Alencar, Manfredo do Carmo, and Renato Tribuzy. A HOPF THEOREM FOR AMBIENT SPACES OF DIMENSIONS HIGHER THAN THREE. 2010. Vol. 84. In Journal of Differential Geometry. pp.1-17. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911204258077065810.
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