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A finiteness theorem for harmonic maps into Hilbert Grassmannians


Author: Rodrigo P. Gomez
Journal: Trans. Amer. Math. Soc. 353 (2001), 1741-1753
MSC (2000): Primary 58E20; Secondary 53C07
Published electronically: January 10, 2001
MathSciNet review: 1637074
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Abstract | References | Similar Articles | Additional Information

Abstract:

In this article we demonstrate that every harmonic map from a closed Riemannian manifold into a Hilbert Grassmannian has image contained within a finite-dimensional Grassmannian.


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Additional Information

Rodrigo P. Gomez
Affiliation: Comprehensive Studies Program, University of Michigan, Ann Arbor, Michigan 48109
Address at time of publication: 8838 Tides Ebb Ct., Columbia, Maryland 21045
Email: rpgomez@yahoo.com

DOI: https://doi.org/10.1090/S0002-9947-01-02420-5
Keywords: Harmonic maps, closed Riemannian manifolds
Received by editor(s): May 22, 1997
Received by editor(s) in revised form: July 15, 1998
Published electronically: January 10, 2001
Additional Notes: I would like to thank D. Burns for suggesting this problem to me.
Dedicated: This article is dedicated to my beloved daughter Katherine
Article copyright: © Copyright 2001 American Mathematical Society