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A remark on vanishing geodesic distances in infinite dimensions


Authors: Valentino Magnani and Daniele Tiberio
Journal: Proc. Amer. Math. Soc. 148 (2020), 3653-3656
MSC (2010): Primary 58B20; Secondary 53C22, 53C23
DOI: https://doi.org/10.1090/proc/14986
Published electronically: March 4, 2020
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Abstract: We observe that a vanishing geodesic distance arising from a weak Riemannian metric in a Hilbert manifold can be constructed.


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Additional Information

Valentino Magnani
Affiliation: Dipartimento di Matematica, Università di Pisa, 56127 Pisa, Italy
Email: valentino.magnani@unipi.it

Daniele Tiberio
Affiliation: Dipartimento di Matematica, Università di Pisa, 56127 Pisa, Italy
Email: danieletiberio@gmail.com

DOI: https://doi.org/10.1090/proc/14986
Keywords: Geodesic distance, Hilbert manifold, weak Riemannian metric
Received by editor(s): October 23, 2019
Received by editor(s) in revised form: December 13, 2019
Published electronically: March 4, 2020
Additional Notes: The first author was supported by the University of Pisa, Project PRA 2018 49.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2020 American Mathematical Society