Almost invariant submanifolds for compact group actions

  • Alan Weinstein

    University of California, Berkeley, United States


Abstract. We define a C1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney's idea of realizing submanifolds as zeros of sections of extended normal bundles.

Cite this article

Alan Weinstein, Almost invariant submanifolds for compact group actions. J. Eur. Math. Soc. 2 (2000), no. 1, pp. 53–86

DOI 10.1007/S100970050014