We introduce a new class of artinian weighted complete intersections, by abstracting the essential features of Q-cohomology algebras of equal rank homogeneous spaces of compact connected Lie groups. We prove that, on a 1-connected closed manifold M with H*(M,Q) belonging to this class, every isometry has a nontrivial invariant geodesic, for any metric on M. We use Q-surgery to construct large classes of new examples for which the above result may be applied.
"Isometry-invariant geodesics and nonpositive derivations of the cohomology." J. Differential Geom. 71 (1) 159 - 176, September 2005. https://doi.org/10.4310/jdg/1143644315