Abstract
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.
Citation
Dorel Fetcu. "Surfaces with parallel mean curvature vector in complex space forms." J. Differential Geom. 91 (2) 215 - 232, June 2012. https://doi.org/10.4310/jdg/1344430822
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