- ¡En oferta!
Hipersuperficies con curvaturas principais constantes nos espazos proxectivo e hiperbólico complexos
- Autor/a
- Domínguez Vázquez, Miguel
A homogeneous submanifold of a Riemannian manifold is an orbit of the action of a closed subgroup of the isometry group of the ambient manifold. Of particular interest are homogeneous hypersurfaces, which arise as principal orbits of cohomogeneity one actions. An important problem in submanifold geometry is to classify homogeneous submanifolds of a given Riemannian manifold and to characterize them in terms of geometric data. A hypersurface has constant principal curvatures if the eigenvalues of its shape operator are constant. Obviously, homogeneous hypersurfaces have constant principal curvatures. It is still an outstanding open problem to determine under which circumstances hypersurfaces with constant principal curvatures of a Riemannian manifold are open parts of homogeneous ones.
Ficha técnica
- Edición
- 1
- Lugar de publicación
- Santiago de Compostela
- Año publicación
- 11/08/2010
- Serie
- Publicaciones del Departamento de Geometría y Topología
- ISBN
- 9788489390355
- Disponibilidad
- Si
A homogeneous submanifold of a Riemannian manifold is an orbit of the action of a closed subgroup of the isometry group of the ambient manifold. Of particular interest are homogeneous hypersurfaces, which arise as principal orbits of cohomogeneity one actions. An important problem in submanifold geometry is to classify homogeneous submanifolds of a given Riemannian manifold and to characterize them in terms of geometric data. A hypersurface has constant principal curvatures if the eigenvalues of its shape operator are constant. Obviously, homogeneous hypersurfaces have constant principal curvatures. It is still an outstanding open problem to determine under which circumstances hypersurfaces with constant