Real hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces

1. 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 workwith J. C. Díaz Ramos) Departament of Geometry and Topology University of Santiago de Compostela

2. Contents

3. Introduction Homogeneous hypersurfaces vs. hypersurfaces with constant principal curvatures ?

4. Introduction The problem in space forms

5. Introduction The problem in complex space forms

6. Introduction The problem in complex space forms g g h h ? ? ? ?

7. as a symmetric space Root space and Iwasawa decompositions

8. as a symmetric space The submanifolds W2n-k

9. Main Theorem

10. Main Theorem Idea of the proof

11. Main Theorem

12. Contents

13. Main Theorem Idea of the proof