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Hipersuperficies con curvaturas principais constantes en variedades Kähler con curvatura seccional holomorfa constante
- Autor/a
- Rodríguez Vázquez, Alberto
A hypersurface in a Riemannian manifold has constant principal curvatures if the eigenvalues of its shape operator do not depend on the point. The problem of classifying hypersurfaces with constant principal curvatures in the complex projective and hyperbolic spaces remains open. The Hopf vector field of a hypersurface in an almost complex manifold is obtained by applying the almost complex structure of the manifold to the normal vector field of the hypersurface. In this work we classify hypersurfaces with four principal curvatures in the complex projective and hyperbolic spaces whose Hopf vector field has non-trivial projection onto three curvature spaces of dimension one.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 2019
- Serie
- 140 Publicaciones del Departamento de Geometría y Topología
- Availability
- Si
A hypersurface in a Riemannian manifold has constant principal curvatures if the eigenvalues of its shape operator do not depend on the point. The problem of classifying hypersurfaces with constant principal curvatures in the complex projective and hyperbolic spaces remains open. The Hopf vector field of a hypersurface in an almost complex manifold is obtained by applying the almost complex structure of the manifold to the normal vector field of the hypersurface. In this work we classify hypersurfaces with four principal curvatures in the complex projective and hyperbolic spaces whose Hopf vector field has non-trivial projection onto three curvature spaces of dimension one.