DIGITAL BOOKSHOP OF THE USC
Foliaciones polares homogéneas en espacios simétricos
- Autor/a
- Lorenzo Naveiro, Juan Manuel
An isometric action of a Lie group on a Riemannian manifold is said to be polar if there exists a submanifold that meets all orbits perpendicularly. Since their first appearance in Conlon's work, it has been an open problem to classify such actions in several families of ambient manifolds, most notably symmetric spaces. In this work we will give an introduction to both symmetric spaces and polar actions, focusing on those without singular orbits and where the ambient space is a symmetric space of noncompact type. Furthermore, we will classify all homogeneous polar foliations on SL(3;R)=SO(3), the space of all volume-preserving, self-adjoint and positive definite linear transformations of R3.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 2022
- Serie
- 149b Publicaciones del Departamento de Geometría y Topología
- Availability
- Si
An isometric action of a Lie group on a Riemannian manifold is said to be polar if there exists a submanifold that meets all orbits perpendicularly. Since their first appearance in Conlon's work, it has been an open problem to classify such actions in several families of ambient manifolds, most notably symmetric spaces. In this work we will give an introduction to both symmetric spaces and polar actions, focusing on those without singular orbits and where the ambient space is a symmetric space of noncompact type. Furthermore, we will classify all homogeneous polar foliations on SL(3;R)=SO(3), the space of all volume-preserving, self-adjoint and positive definite linear transformations of R3.