Isometry-invariant geodesics and nonpositive derivations of the cohomology

Details Isometry-invariant geodesics and nonpositive derivations of the cohomology Isometry-invariant geodesics and nonpositive derivations of the cohomology

2003-11-20

arxiv.org/abs/math/0311340v1

J. Differential Geometry 71 (2005), 159-176

Mathematics

Differential Geometry

14 pages

Scientific paper

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.

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