Slice rigidity property of holomorphic maps Kobayashi-isometrically\n preserving complex geodesics

2020/12/26 by Filippo Bracci, Łukasz Kosiński, Bracci, Filippo +3 · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2012.13701

openalex publication_date 2020/12/26 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper we study the following "slice rigidity property": given two\nKobayashi complete hyperbolic manifolds M, N and a collection of complex\ngeodesics mathcal F of M, when is it true that every holomorphic map\nF:M\→ N which maps isometrically every complex geodesic of mathcal F onto\na complex geodesic of N is a biholomorphism? Among other things, we prove\nthat this is the case if M, N are smooth bounded strictly (linearly) convex\ndomains, every element of mathcal F contains a given point of \M\nand mathcal F spans all of M. More general results are provided in\ndimension 2 and for the unit ball.\n

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