Isometryinvariant geodesics and nonpositive derivations of the cohomology
Abstract
We introduce a new class of zerodimensional weighted complete intersections, by abstracting the essential features of rational cohomology algebras of equal rank homogeneous spaces of compact connected Lie groups. We prove that, on a 1connected closed manifold M whose rational cohomology algebra belongs to this class, every isometry has a nontrivial invariant geodesic, for any metric on M. We use rational surgery to construct large classes of new examples for which the above result may be applied.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2003
 arXiv:
 arXiv:math/0311340
 Bibcode:
 2003math.....11340P
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Topology;
 53C22;
 13C40 (primary);
 57T15;
 55P62;
 57R65 (secondary)
 EPrint:
 14 pages