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(1, 2)-SYMPLECTIC METRICS, FLAG MANIFOLDS AND TOURNAMENTS

Published online by Cambridge University Press:  24 March 2003

NIR COHEN ,
CAIO J. C. NEGREIROS  and
LUIZ A. B. SAN MARTIN
NIR COHEN
Affiliation:
Institute of Mathematics (Imecc), Universidade Estadual de Campinas, Cx. Postal 6065, 13.083-970, Campinas – SP, Brazilsmartin@ime.unicamp.br
CAIO J. C. NEGREIROS
Affiliation:
Institute of Mathematics (Imecc), Universidade Estadual de Campinas, Cx. Postal 6065, 13.083-970, Campinas – SP, Brazilsmartin@ime.unicamp.br
LUIZ A. B. SAN MARTIN
Affiliation:
Institute of Mathematics (Imecc), Universidade Estadual de Campinas, Cx. Postal 6065, 13.083-970, Campinas – SP, Brazilsmartin@ime.unicamp.br
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Abstract

It has recently been shown by Mo and Negreiros that a necessary condition for an invariant almost complex structure on the complex full flag manifold ${\bb F}(n)$ to admit a (1, 2)-symplectic invariant metric is that its associated tournament be cone-free. In this paper, a canonical stair-shaped form is given for such tournaments, and this is applied to show that the condition is also sufficient; in the process, all the associated (1, 2)-symplectic metrics are described.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 6 , November 2002 , pp. 641 - 649
Copyright
© The London Mathematical Society 2002

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Footnotes

First and third authors supported by CNPq grants 300019/96-3 and 301060/94-0 respectively.