2002/01/15 by Imre Major, Major, Imre
Mathematics · #57M70 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GR #msc:57M70
paper · pdf · doi:10.48550/arxiv.math/0201133
11 pages
arxiv created 2002/01/15 · openalex publication_date 2002/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We will prove the equivariant version of Smale's transversality theorem: suppose that the compact Lie-group G acts on the compact differentiable manifold M on which an invariant Morse-function f and an invariant vector field X are given so that X is gradient-like with respect to f (i.e. X(f)<0 away from critical orbits and X is the gradient of f (w.r.t. a fixed invariant Riemannian metric) on some invariant open subsets about critical orbits of f.) Given a bound ε>0 we will prove the existence of an invariant vector field Y of class C1 for which vector field X+Y is also gradient-like such that: (a) |Y|1