Da rigidez de variedades kählerianas munidas de campo vetorial conforme fechado.

• Autor(a) principal: Xavier, Valricélio Menezes
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/50768
• topic: Variedades kählerianas; Campo conforme fechado; Curvatura não positiva; Toro plano; Campos paralelos; Kählerian manifolds; Closed conformal vector fields; Nonpositive curvature; Flat torus; Parallel vector fields

The goal of this work is to demonstrate two results about the rigidity of kählerian manifolds under certain conditions. In the first result, we show that if a connected compact kählerian surface M with nonpositive gaussian curvature is endowed with a closed conformal vector field ξ whose singular points are isolated, then M has necessarily zero gaussian curvature, ξ is parallel and M is isometric to a flat torus. In the second result, we consider a connected complete kählerian manifold M, of complex dimension n > 1 and equipped with a nontrivial closed conformal vector field ξ. In this case, if the distribution D in M \ ξ −1 (0), generated by ξ and Jξ, has one compact leaf Σ with nonpositive holomorphic sectional curvature and Hol ⊥ (Σ) is a torsion group, then ξ −1 (0) = ∅, ξ and Jξ are parallel in M, the leafs of D are isometric to the flat torus and the leafs of D ⊥ are isometric to a kählerian manifold of complex dimension n − 1. In particular, the universal covering of M is a cartesian product of R2 with a connected, simply connected, complete kählerian manifold.