J. Aust. Math. Soc.
74 (2003), 239-248
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An integral formula for compact hypersurfaces in space forms and its applications
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Luis J. Alías
Departamento de Matemáticas
Universidad de Murcia
E-30100 Espinardo, Murcia
Spain
ljalias@um.es
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Abstract
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In this paper we establish an integral formula
for compact hypersurfaces in non-flat space
forms, and apply it to derive some interesting
applications. In particular, we obtain a
characterization of geodesic spheres in terms of
a relationship between the scalar curvature of
the hypersurface and the size of its Gauss map
image. We also derive an inequality involving the
average scalar curvature of the hypersurface and
the radius of a geodesic ball in the ambient
space containing the hypersurface, characterizing
the geodesic spheres as those for which equality
holds.
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