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Geometric consequences of algebraic conditions on curvature operators
- Autor/a
- Brozos Vázquez, Miguel
As a Riemannian invariant, the curvature and its derivatives are the
most natural algebraic invariants which stem from the connection.
Therefore, this suggests that the curvature encodes a lot of
information of the geometry of a Riemannian manifold. These
considerations show that the curvature is a fundamental concept in
diferential geometry, nevertheless the role played by this important
tensor is not yet completely understood. The main purpose of this
thesis is to obtain geometric consequences from algebraic conditions
on the curvature tensor. Usually, we will impose these conditions on
operators associated to the curvature tensor, since the curvature
tensor itself is hard to handle. Generally we work in the broad
setting of pseudo-Riemannian manifolds; however, in some chapters or
sections we will restrict our analysis to positive definite metrics.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Editorial
- Universidade de Santiago de Compostela. Servizo de Publicacións e Intercambio Científico
- Publication Year
- 20/09/2007
- File Size
- 1.3 MB
- Serie
- Publicaciones del Departamento de Geometría y Topología
- ISBN
- 9788489390263
- Availability
- Si
As a Riemannian invariant, the curvature and its derivatives are the
most natural algebraic invariants which stem from the connection.
Therefore, this suggests that the curvature encodes a lot of
information of the geometry of a Riemannian manifold. These
considerations show that the curvature is a fundamental concept in
diferential geometry, nevertheless the role played by this important
tensor is not yet completely understood. The main purpose of this
thesis is to obtain geometric consequences from algebraic conditions
on the curvature tensor. Usually, we will impose these conditions on
operators associated to the curvature tensor, since the curvature
tensor itself is hard to handle. Generally we work in the broad
setting of pseudo-Rieman...