Surfaces with parallel mean curvature vector in and
Authors:
Francisco Torralbo and Francisco Urbano
Journal:
Trans. Amer. Math. Soc. 364 (2012), 785813
MSC (2010):
Primary 53A10; Secondary 53B35
Published electronically:
October 3, 2011
MathSciNet review:
2846353
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Abstract: Two holomorphic Hopf differentials for surfaces of nonnull parallel mean curvature vector in and are constructed. A 1:1 correspondence between these surfaces and pairs of constant mean curvature surfaces of and is established. Using this, surfaces with vanishing Hopf differentials (in particular, spheres with parallel mean curvature vector) are classified and a rigidity result for constant mean curvature surfaces of and is proved.
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Additional Information
Francisco Torralbo
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email:
ftorralbo@ugr.es
Francisco Urbano
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email:
furbano@ugr.es
DOI:
http://dx.doi.org/10.1090/S000299472011053468
Received by editor(s):
December 30, 2008
Received by editor(s) in revised form:
October 27, 2009, and February 15, 2010
Published electronically:
October 3, 2011
Additional Notes:
This research was partially supported by an MCyTFeder research project MTM200761775 and a Junta Andalucĭa Grant P06FQM01642.
Article copyright:
© Copyright 2011
American Mathematical Society
