Clasificación de los espacios simétricos con estructura de variedad Flag compleja y sus fibrados cotangentes - García Rojas, Ada Carolina (2023)
The basis of this work is the study of the symmetry of complex Flag manifolds_x000D_ FΘ U{UΘ, as well as the adjoint orbits (símbolos) from the point of view shown in_x000D_ [1]. The adjoint orbit has a realization as a cotangent bundle of a Flag manifold FΘ;_x000D_ this realization is the main motivation of this study. The goals of this work are to_x000D_ classify flag manifolds that present structure of symmetric spaces and to show that_x000D_ cotangent bundles of such manifolds are also symmetric spaces. The symmetry of_x000D_ these spaces allows to provide a new structure to the adjoint orbit, which broadens its_x000D_ geometrical properties. This study generates new questions about which geometric_x000D_ properties are projected from the fiber bundle to the Flag manifold. On the other_x000D_ hand, there are classifications of symmetric spaces as homogeneous spaces given_x000D_ in [4] and [7]. These classifications allowed us to verify our results. Finally, we_x000D_ classify the complex Flag manifolds that are symmetric spaces and it is shown that_x000D_ the cotangent bundle of these spaces are also symmetric spaces. The results are_x000D_ obtained by defining specific involutions for each case as well as the realization of_x000D_ Flag manifolds as homogeneous spaces.