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On the Gauss map of hypersurfaces with constant scalar curvature in spheres
Author(s):
Hilário
Alencar;
Harold
Rosenberg;
Walcy
Santos
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3731-3739.
MSC (2000):
Primary 53C40;
Secondary 53A10
Posted:
July 12, 2004
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Abstract:
In this work we consider connected, complete and orientable hypersurfaces of the sphere  with constant nonnegative  -mean curvature. We prove that under subsidiary conditions, if the Gauss image of  is contained in a closed hemisphere, then  is totally umbilic.
References:
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Additional Information:
Hilário
Alencar
Affiliation:
Departamento de Matemática, Universidade Federal de Alagoas, 57072-900, Maceió, AL, Brazil
Email:
hilario@mat.ufal.br
Harold
Rosenberg
Affiliation:
Institut de Mathématiques de Jussieu, 2 Place Jussieu, 75251 Paris, France
Email:
rosen@math.jussieu.fr
Walcy
Santos
Affiliation:
Departamento de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil
Email:
walcy@im.ufrj.br
DOI:
10.1090/S0002-9939-04-07493-3
PII:
S 0002-9939(04)07493-3
Keywords:
$r$-mean curvature,
spheres,
Gauss image
Received by editor(s):
April 28, 2003
Received by editor(s) in revised form:
September 1, 2003
Posted:
July 12, 2004
Additional Notes:
The first and third authors' research was partially supported by CNPq and the French-Brazilian Agreement in Mathematics
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2004,
American Mathematical Society
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