Surfaces with parallel mean curvature vector in and
Authors:
Francisco Torralbo and Francisco Urbano
Journal:
Trans. Amer. Math. Soc. 364 (2012), 785-813
MSC (2010):
Primary 53A10; Secondary 53B35
DOI:
https://doi.org/10.1090/S0002-9947-2011-05346-8
Published electronically:
October 3, 2011
MathSciNet review:
2846353
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Abstract | References | Similar Articles | Additional Information
Abstract: Two holomorphic Hopf differentials for surfaces of non-null 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:
https://doi.org/10.1090/S0002-9947-2011-05346-8
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 MCyT-Feder research project MTM2007-61775 and a Junta Andalucĭa Grant P06-FQM-01642.
Article copyright:
© Copyright 2011
American Mathematical Society