1999/10/07 by Andrea Spiro, Spiro, Andrea
Mathematics · Physics and Astronomy · #32H15 #53A55 #53B15 #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Primary 53B40 #Secondary 53C60 #math.CV #math.DG #msc:32H15 #msc:53A55 #msc:53B15 #msc:53B40 #msc:53C60
paper · pdf · doi:10.48550/arxiv.math/9910040
arxiv created 1999/10/07 · openalex publication_date 1999/10/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a strongly pseudo-convex complex Finsler manifold M, a bundle U of adapted unitary frames is canonically defined. A non-linear Hermitian connection on U, invariant under local biholomorphic isometries, is given and it proved to be unique. By means of such connection, an absolute parallelism on U is determined and a new set of structure functions which generate all the isometric invariants of a Finsler metric is obtained. A pseudo-convex complex Finsler manifolds M, which admits a totally geodesic complex curve with a given constant holomorphic sectional curvature through any point and any direction, is called E-manifold. Main examples of E-manifolds are the smoothly bounded, strictly convex domains in Cn, endowed with the Kobayashi metric. A complete characterization of E-manifolds, using the previously defined structure functions, is given and a smaller set of generating functions for the isometric invariants of E-manifolds is determined.