Minkowski identities for hypersurfaces in constant sectional curvature manifolds

• Main Author: Albuquerque, Rui
• Publication Date: 2019
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/10174/26876; https://doi.org/Rui Albuquerque, Minkowski identities for hypersurfaces in constant sectional Curvature manifolds, Differential Geometry and its Applications, Volume 67, 2019, 101561, ISSN 0926-2245, https://doi.org/10.1016/j.difgeo.2019.101561; https://doi.org/10.1016/j.difgeo.2019.101561
• topic: sistemas diferenciais; hipersuperfícies; Curvatura média; identidades integrais

We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental differential system of Riemannian geometry introduced by the author. We develop the notion of position vector field, which lies at the core of the Minkowski identities.