RT Journal Article
T1 The Ambrose-Singer Theorem for general homogeneous manifolds with applications to symplectic geometry
A1 Carmona Jiménez, José Luis
A1 Castrillón López, Marco
AB The main Theorem of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (not necessarily pseudo-Riemannian) in terms of the existence of certain connection. This result generalizes the well-known Theorem of Ambrose and Singer for Riemannian homogeneous spaces (Ambrose and Singer in Duke Math J 25(4):647–669, 1958). We relax the conditions in this theorem and prove a characterization of reductive locally homogeneous manifolds. Finally, we apply these results to classify, with explicit expressions, reductive locally homogeneous almost symplectic, symplectic and Fedosov manifolds.
PB Springer
YR 2022
FD 2022
LK https://hdl.handle.net/20.500.14352/128341
UL https://hdl.handle.net/20.500.14352/128341
LA eng
NO Carmona Jiménez, J.L., Castrillón López, M. The Ambrose–Singer Theorem for General Homogeneous Manifolds with Applications to Symplectic Geometry. Mediterr. J. Math. 19, 280 (2022).
NO 2022 Acuerdos transformativos CRUE
NO Ministerio de Ciencia, Innovación y Universidades
NO Junta de Castilla y León
DS Docta Complutense
RD 31 dic 2025