In this paper, we study the following “slice rigidity property”: given two Kobayashi complete hyperbolic manifolds M, N and a collection of complex geodesics F of M, when is it true that every holomorphic map F : M → N which maps isometrically every complex geodesic of F onto a complex geodesic of N is a biholomorphism? Amongotherthings,weprovethatthisisthecaseif M, N aresmoothboundedstrictly (linearly) convex domains, every element of F contains a given point of M and F spans all of M. More general results are provided in dimension 2 and for the unit ball.
Bracci, F., Kosiński, Ł., Zwonek, W. (2021). Slice rigidity property of holomorphic maps Kobayashi-isometrically preserving complex geodesics. THE JOURNAL OF GEOMETRIC ANALYSIS, 31(11), 11292-11311 [10.1007/s12220-021-00681-6].
Slice rigidity property of holomorphic maps Kobayashi-isometrically preserving complex geodesics
Bracci, Filippo;
2021-05-10
Abstract
In this paper, we study the following “slice rigidity property”: given two Kobayashi complete hyperbolic manifolds M, N and a collection of complex geodesics F of M, when is it true that every holomorphic map F : M → N which maps isometrically every complex geodesic of F onto a complex geodesic of N is a biholomorphism? Amongotherthings,weprovethatthisisthecaseif M, N aresmoothboundedstrictly (linearly) convex domains, every element of F contains a given point of M and F spans all of M. More general results are provided in dimension 2 and for the unit ball.File | Dimensione | Formato | |
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