On a monodromy theorem for sheaves of local fields and applications

Autor(es)

Herrera, Jonatan ; Angel Javaloyes, Miguel ; Piccione, Paolo

• Tipo de documento: Artigo Científico
• Fonte: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS; v. 111, n. 4, p. 999-1029, OCT 2017.
• Citações Web of Science: 2

Resumo

We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we obtain a global extension result for every local field of the sheaf. This generalizes previous works of Nomizu (Ann Math (2) 72:105-120 {[}28]) for semi-Riemannian Killing fields, of Ledger-Obata (Trans Amer Math Soc 150:645-651 {[}26]) for conformal fields, and of Amores (J Differ Geom 14(1):1-6 {[}1]) for fields preserving a G-structure of finite type. Among the new applications of our result, we will consider the case of Finsler and pseudo-Finsler Killing fields, and, more generally, the case of affine fields for a spray. Some applications are discussed. (AU)

• Processo FAPESP: 12/11950-7 - Tópicos em Relatividade Matemática
• Beneficiário: Jónatan Herrera Fernández
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado