Steepest Descent on Real Flag Manifolds |
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| Authors: | Eschenburg J-H; Mare A-L |
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| Institution: | Institut für Mathematik, Universität Augsburg D-86135 Augsburg, Germany eschenburg{at}math.uni-augsburg.de
Department of Mathematics and Statistics, University of Regina Regina SK, Canada S4S 0A2 mareal{at}math.uregina.ca |
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| Abstract: | Real flag manifolds are the isotropy orbits of noncompact symmetricspaces G/K. Any such manifold M is acted on transitively bythe (noncompact) Lie group G, and it is embedded in euclideanspace as a taut submanifold. The aim of this paper is to showthat the gradient flow of any height function is a one-parametersubgroup of G, where the gradient is defined with respect toa suitable homogeneous metric s on M; this generalizes the Kählermetric on adjoint orbits (the so-called complex flag manifolds).2000 Mathematics Subject Classification 53C30, 53C35. |
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