Steepest descent on real flag manifolds

Details Steepest descent on real flag manifolds Steepest descent on real flag manifolds

2002-08-02

arxiv.org/abs/math/0208018v2

Mathematics

Differential Geometry

This is a substantially revised version of the paper entitled initially "Flow lines on isotropy orbits". It has 8 pages

Scientific paper

Real flag manifolds are the isotropy orbits of noncompact symmetric spaces $G/K$. Any such manifold $M$ enjoys two very peculiar geometric properties: It carries a transitive action of the (noncompact) Lie group $G$, and it is embedded in euclidean space as a taut submanifold. The aim of the paper is to link these two properties by showing 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 Kaehler metric on adjoint orbits (the so-called complex flag manifolds).

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