Wilkins, D. R. Infinite-dimensional homogeneous manifolds. (English) Zbl 0814.58007 Proc. R. Ir. Acad., Sect. A 94, No. 1, 105-118 (1994). First, the author generalizes the Cartan-Ambrose-Hicks theorem to smooth Banach manifolds. Using it he characterizes the simply-connected symmetric manifolds as smooth Banach manifolds admitting a geodesically complete torsion-free affine connection whose curvature tensor is parallel. Then he proves an integrability theorem for invariant almost complex structures on any symmetric Banach manifold that admits an invariant Finsler structure. Various consequences of this are discussed. Reviewer: M.Anastasiei (Iaşi) Cited in 5 Documents MSC: 58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:symmetric spaces; almost complex structures; Finsler structure PDFBibTeX XMLCite \textit{D. R. Wilkins}, Proc. R. Ir. Acad., Sect. A 94, No. 1, 105--118 (1994; Zbl 0814.58007)