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Surfaces with parallel mean curvature vector in complex space forms

Dorel Fetcu Department of Mathematics and Informatics

Differential Geometry mathscidoc:1609.10269

Journal of Differential Geometry, 91, (2), 215-232, 2012
We consider surfaces with parallel mean curvature vector (pmc surfaces) in complex space forms and introduce a holomorphic differential on such surfaces. When the complex dimension of the ambient space is equal to two we find a second holomorphic differential and then determine those pmc surfaces on which both differentials vanish. We also provide a reduction of codimension theorem and prove a non-existence result for pmc 2-spheres in complex space forms.
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@inproceedings{dorel2012surfaces,
  title={SURFACES WITH PARALLEL MEAN CURVATURE VECTOR IN COMPLEX SPACE FORMS},
  author={Dorel Fetcu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913230045035745931},
  booktitle={Journal of Differential Geometry},
  volume={91},
  number={2},
  pages={215-232},
  year={2012},
}
Dorel Fetcu. SURFACES WITH PARALLEL MEAN CURVATURE VECTOR IN COMPLEX SPACE FORMS. 2012. Vol. 91. In Journal of Differential Geometry. pp.215-232. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913230045035745931.
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