Workshop on Hypersurface Geometry and Integrable Systems
Sendai 2010
Real hypersurfaces with
constant principal curvatures
in complex projective and
hyperbolic spaces
Miguel Domínguez Vázquez (joint work with J. C. Díaz Ramos)
Departament of Geometry and Topology
University of Santiago de Compostela
Contents
Introduction
Homogeneous hypersurfaces vs. hypersurfaces
with constant principal curvatures
Introduction
The problem in space forms
Introduction
The problem in complex space forms
Introduction
g
h
1
2
3
The problem in complex space forms
4
5
>5
g
h
1
1
2
2
3
3
4
4
5
5
>5
>5
?
1
2
3
4
?
?
5
?
>5
as a symmetric space
Root space and Iwasawa
decompositions
as a symmetric space
The submanifolds W2n-k
Main Theorem
Main Theorem
Idea of the proof
Main Theorem
Contents
Main Theorem
Idea of the proof