DIGITAL BOOKSHOP OF THE USC
Teoremas de Cartan y Münzner para hipersuperficies isoparamétricas en esferas
- Autor/a
- Peñate Moreno, Fernando
This work focuses on the study of isoparametric hypersurfaces in spheres. We begin by introducing the concept of isoparametric hypersurface, and we analyze its relation with the notion of homogeneous hypersurface. Moreover, we include some results characterizing isoparametric hypersurfaces in spaces of constant curvature. Then, we study these geometric objects in spherical spaces. We introduce Munzner's structure theory for isoparametric hypersurfaces in spheres, proving his remarkable algebraicity result, which states that these objects can be obtained from a certain kind of homogeneous polynomials, the so-called Cartan-Munzner polynomials. We discuss the classication problem in spheres, describing some examples and important results. Finally, we include a partially original proof of Cartan's homogeneity and classication result of isoparametric hypersurfaces with three principal curvatures in spheres.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 2022
- Serie
- 150a Publicaciones del Departamento de Geometría y Topología
- Availability
- Si
This work focuses on the study of isoparametric hypersurfaces in spheres. We begin by introducing the concept of isoparametric hypersurface, and we analyze its relation with the notion of homogeneous hypersurface. Moreover, we include some results characterizing isoparametric hypersurfaces in spaces of constant curvature. Then, we study these geometric objects in spherical spaces. We introduce Munzner's structure theory for isoparametric hypersurfaces in spheres, proving his remarkable algebraicity result, which states that these objects can be obtained from a certain kind of homogeneous polynomials, the so-called Cartan-Munzner polynomials. We discuss the classication problem in spheres, describing some examples and important results. Fina