Copolarity of isometric actions

Authors:
Claudio Gorodski, Carlos Olmos and Ruy Tojeiro

Journal:
Trans. Amer. Math. Soc. **356** (2004), 1585-1608

MSC (2000):
Primary 57S15; Secondary 53C20

DOI:
https://doi.org/10.1090/S0002-9947-03-03427-5

Published electronically:
September 22, 2003

MathSciNet review:
2034320

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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a new integral invariant for isometric actions of compact Lie groups, the *copolarity*. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In particular, we develop some of the structural theory of copolarity representations, we classify the irreducible representations of copolarity one, and we relate the copolarity of an isometric action to the concept of variational completeness in the sense of Bott and Samelson.

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Additional Information

**Claudio Gorodski**

Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP 05508-090, Brazil

Email:
gorodski@ime.usp.br

**Carlos Olmos**

Affiliation:
Facultad de Matemática, Astronomía y Física, Universidad Nacional Córdoba, Medina Allende y Haya de la Torre, Ciudad Universitaria, 5000 Córdoba, Argentina

Email:
olmos@mate.uncor.edu

**Ruy Tojeiro**

Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, Rodovia Washington Luiz, Km 235, São Carlos, SP 13565-905, Brazil

Email:
tojeiro@dm.ufscar.br

DOI:
https://doi.org/10.1090/S0002-9947-03-03427-5

Received by editor(s):
October 17, 2002

Received by editor(s) in revised form:
March 3, 2003

Published electronically:
September 22, 2003

Additional Notes:
The first author was supported in part by CNPq grant 300720/93-9 and by FAPESP grant 01/04793-8.

The second author was supported by Universidad Nacional de Córdoba and CONICET, and supported in part by CIEM, Secyt-UNC and ANPCYT

The third author was supported in part by CNPq grant 300229/92-5 and FAPESP grant 01/05318-1.

Article copyright:
© Copyright 2003
American Mathematical Society