Isometry-invariant geodesics and nonpositive derivations of the cohomology

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We introduce a new class of zero-dimensional 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 1-connected closed manifold M whose rational cohomology algebra belongs to this class, every isometry has a non-trivial 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.
14 pages

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Differential Geometry, Algebraic Topology, 53C22, 13C40 (primary); 57T15, 55P62, 57R65 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/143934

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311340
 http://arxiv.org/abs/math/0311340
 J. Differential Geometry 71 (2005), 159-176

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arXiv