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Bounded mean curvature isometric immersions of a compact Riemannian manifold with images contained in a tube

Published online by Cambridge University Press:  18 May 2009

Francisco J. Carreras ,
Fernando Giménez  and
Vicente Miquel
Francisco J. Carreras
Affiliation:
Departamento de Geometria y TopologiáUniversidad de Valencia Burjasot, ValenciaSpaine-mail: carreras@uv.es
Fernando Giménez
Affiliation:
Departamento de Matemática AplicadaE.T.S.I. IndustrialesUniversidad Politécnica de ValenciaSpain e-mail: fgimenez@mat.upv.es.
Vicente Miquel
Affiliation:
Departamento de Geometría y TopologíUniversidad de Valencia Burjasot, ValenciaSpain e-mail: miquel@uv.es
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Abstract

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We characterize some isometric immersions of a compact Riemannian manifold into a tube of Sn(λ) or CPn(λ) (in fact, in some more general spaces in the real case) around a totally geodesic Sq(λ) or CPq(λ) respectively, with the norm of the mean curvature of the immersion bounded from above. This bound depends on the radius of the tube, and is related with the mean curvature of its boundary.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 1 , March 1998 , pp. 97 - 107
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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