Curvatura y fibrados principales sobre el círculo (Curvature and principal S 1 -bundles)
The aim of this thesis is to study in detail the work of S. Kobayashi on the Riemannian geometry on principal S1-bundles. To be more precise, we explain how to obtain metrics with constant scalar curvature on these bundles. The method that we use is based in [18]. The basic idea behind Kobayashi...
| Autor Principal: | Lope Vicente, Joe Moises |
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| Formato: | Tesis de Maestría |
| Idioma: | Inglés |
| Publicado: |
Pontificia Universidad Católica del Perú
2018
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| Materias: | |
| Acceso en línea: |
http://tesis.pucp.edu.pe/repositorio/handle/123456789/12829 |
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| Sumario: |
The aim of this thesis is to study in detail the work of S. Kobayashi on the
Riemannian geometry on principal S1-bundles. To be more precise, we explain
how to obtain metrics with constant scalar curvature on these bundles. The
method that we use is based in [18].
The basic idea behind Kobayashi’s construction is to slightly deform the
Hopf fibration S1 ‹→ S2n+1 −→ CPn in a such a way that the corresponding
sectional curvatures are not far from the produced by the standard metrics
on the sphere and the complex projective space on the Hopf fibration. This
deformations can be controlled applying the notions of Riemaniann and
Kahlerian pinching (see Chapter 3).
Furthermore, thanks to a technique developed by Hatakeyama in [14], it
is possible to obtain less generic metrics but with a larger set of symmetries
on the total space: Sasaki metrics. Actually, If one chooses as a base space a
K¨ahler-Einstein manifold with positive scalar curvature one can obtain a
Sasaki-Einstein metric. |
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