Open Access
June 2012 Surfaces with parallel mean curvature vector in complex space forms
Dorel Fetcu
J. Differential Geom. 91(2): 215-232 (June 2012). DOI: 10.4310/jdg/1344430822


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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Dorel Fetcu. "Surfaces with parallel mean curvature vector in complex space forms." J. Differential Geom. 91 (2) 215 - 232, June 2012.


Published: June 2012
First available in Project Euclid: 8 August 2012

zbMATH: 1272.53051
MathSciNet: MR2971287
Digital Object Identifier: 10.4310/jdg/1344430822

Rights: Copyright © 2012 Lehigh University

Vol.91 • No. 2 • June 2012
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