Um teorema fundamental para hipersuperfícies em produtos torcidos semi-riemannianos

• Autor(a) principal: Melara Estrada, Mynor Ademar
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/11173
• topic: Hipersuperfície; Produto torcido; Teorema fundamental; Espaço semi-riemanniano; Hypersurface; Warped product; Fundamental theorem; Semi-Riemannian space; CIENCIAS EXATAS E DA TERRA::MATEMATICA

The aim of this dissertation is to show a demonstration of a fundamental theorem for existence of isometric immersions for hypersurfaces in a warped product space where the base is a interval and the fiber is a spatial form, both with semi-Riemannian metrics, and in addition to that, present an application of this theorem for horizons in a Robertson-Walker spacetime of dimension 4, both based on the work of Marie Am´elie Lawn and Miguel Ortega in [J. Geom. Phys. 90 (2015) 55-70]. Such a result, generalizes fundamental theorems for hypersurfaces obtained, by B. Daniel for Riemannian products in [Trans. Amer. Math. Soc. 361 (2009) 6255-6282], by Q. Chen and C.R. Xiang for Riemannian warped products in the case of fibers with zero sectional curvature in [Acta Math. Sinica. 26 (2010) 2269-2282]; and by J. Roht, in the case of Lorentzian products with Riemannian fibers in [Int. J. Geom. Methods Mod. Phys. 8 (2011) 1269-1290]. Also, based on the demonstration of local uniqueness of B. Daniel’s fundamental theorem, we prove that the isometric immersion obtained in Lawn and Ortega’s theorem, is unique up to a global isometry.