Matemáticas (Mag.)
URI permanente para esta colecciónhttp://54.81.141.168/handle/123456789/9102
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Ítem Texto completo enlazado Una representación tipo Weierstrass para superficies mínimas en grupos de Lie(Pontificia Universidad Católica del Perú, 2019-09-23) Condeña Cahuana, Jorge Emiliano; Figueroa Serrudo, Christiam BernardoEn el presente trabajo se introduce el concepto de fibrados vectoriales reales, complejos y holomorfas para conseguir una representación tipo Weierstrass para superficies mínimas e inmersas en grupos de Lie de dimensión 3, con una métrica riemanniana in-variante a izquierda.Ítem Texto completo enlazado Curvatura y fibrados principales sobre el círculo (Curvature and principal S 1 -bundles)(Pontificia Universidad Católica del Perú, 2018-10-04) Lope Vicente, Joe Moises; Cuadros Valle, JaimeThe 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.