Isometries for the Carathéodory metric
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- by Marco Abate and Jean-Pierre Vigué PDF
- Proc. Amer. Math. Soc. 136 (2008), 3905-3909 Request permission
Abstract:
Given two open unit balls $B_1$ and $B_2$ in complex Banach spaces, we consider a holomorphic mapping $f\colon B_1\to B_2$ such that $f(0)=0$ and $f’(0)$ is an isometry. Under some additional hypotheses on the Banach spaces involved, we prove that $f(B_1)$ is a complex closed analytic submanifold of $B_2$.References
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Additional Information
- Marco Abate
- Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Pontecorvo 5, 56127 Pisa, Italy
- Email: abate@dm.unipi.it
- Jean-Pierre Vigué
- Affiliation: LMA, Université de Poitiers, CNRS, Mathématiques, SP2MI, BP 30179, 86962 Futuroscope cedex, France
- Email: vigue@math.univ-poitiers.fr
- Received by editor(s): July 17, 2007
- Received by editor(s) in revised form: September 19, 2007
- Published electronically: May 20, 2008
- Communicated by: Mei-Chi Shaw
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3905-3909
- MSC (2000): Primary 32H02
- DOI: https://doi.org/10.1090/S0002-9939-08-09391-X
- MathSciNet review: 2425730