DIGITAL BOOKSHOP OF THE USC
Subvariedades homoxéneas minimais nos espazos hiperbólicos complexos
- Autor/a
- Cidre Díaz, Ángel
Symmetric spaces constitute a important class of Riemannian manifolds, since their isometry groups have a rich structure. Because of this fact, they turn out to be a class of spaces for which the study of their submanifolds is particularly interesting, especially of those with a high degree of symmetry. On the one hand, the identity component of the isometry group of a symmetric space of non-compact type can be expressed as the product of a compact Lie group and a solvable Lie group. The submanifolds of the symmetric space that are obtained as orbits of a Lie group of such solvable Lie group are called solvable homogeneous submanifolds. On the other hand, an important generalization of the notion of geodesic is that of minimal submanifold: a submanifold whose mean curvature vector field vanishes. The main aim of this memoir is to classify the solvable homogeneous minimal submanifolds of the complex hyperbolic space, which is an example of a symmetric space of non-compact type.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 2024
- Serie
- 154a Publicaciones del Departamento de Geometría y Topología
- Availability
- Si
Symmetric spaces constitute a important class of Riemannian manifolds, since their isometry groups have a rich structure. Because of this fact, they turn out to be a class of spaces for which the study of their submanifolds is particularly interesting, especially of those with a high degree of symmetry. On the one hand, the identity component of the isometry group of a symmetric space of non-compact type can be expressed as the product of a compact Lie group and a solvable Lie group. The submanifolds of the symmetric space that are obtained as orbits of a Lie group of such solvable Lie group are called solvable homogeneous submanifolds. On the other hand, an important generalization of the notion of geodesic is that of minimal submanifold: