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STEEPEST DESCENT ON REAL FLAG MANIFOLDS

Published online by Cambridge University Press:  16 March 2006

J.-H. ESCHENBURG  and
A.-L. MARE
J.-H. ESCHENBURG
Affiliation:
Institut für Mathematik, Universität Augsburg, D-86135 Augsburg, Germanyeschenburg@math.uni-augsburg.de
A.-L. MARE
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina SK, Canada S4S 0A2 mareal@math.uregina.ca
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Abstract

Real flag manifolds are the isotropy orbits of noncompact symmetric spaces $G/K$. Any such manifold $M$ is acted on transitively by the (noncompact) Lie group $G$, and it is embedded in euclidean space as a taut submanifold. The aim of this paper is to show that the gradient flow of any height function is a one-parameter subgroup of $G$, where the gradient is defined with respect to a suitable homogeneous metric $s$ on $M$; this generalizes the Kähler metric on adjoint orbits (the so-called complex flag manifolds).

Keywords

53C3053C35
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 2 , April 2006 , pp. 323 - 328
Copyright
The London Mathematical Society 2006

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