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

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:
http://dx.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