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Steepest Descent on Real Flag Manifolds
Author(s) -
Eschenburg J.H.,
Mare A.L.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018376
Subject(s) - mathematics , flag (linear algebra) , generalized flag variety , manifold (fluid mechanics) , pure mathematics , metric (unit) , submanifold , symmetric space , isotropy , lie group , euclidean space , mathematical analysis , descent (aeronautics) , algebra over a field , mechanical engineering , operations management , physics , quantum mechanics , engineering , economics , aerospace engineering
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 ). 2000 Mathematics Subject Classification 53C30, 53C35.