Isometry-invariant geodesics and nonpositive derivations of the cohomology

@article{Papadima2003IsometryinvariantGA,
  title={Isometry-invariant geodesics and nonpositive derivations of the cohomology},
  author={Stefan Papadima and Laurentiu Paunescu},
  journal={Journal of Differential Geometry},
  year={2003},
  volume={71},
  pages={159-176}
}
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… 
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6 Citations

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References

SHOWING 1-10 OF 23 REFERENCES
Rational homotopy equivalences of Lie type
  • S. Papadima
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1988
Consider K⊂G, a proper pair of equal rank compact connected Lie groups. It is known (see [6], proof of theorem 1·1) that the group of self-homotopy equivalences of the rationalization of G/K is…
The homology theory of the closed geodesic problem
The problem—does every closed Riemannian manifold of dimension greater than one have infinitely many geometrically distinct periodic geodesies—has received much attention. An affirmative answer is…
Characteristic Classes
Let (P,M,G) be a principle fibre bundle over M with group G, connection ω and quotient map π. Recall that for all p ∈ P the Lie algebra G is identified with VpP := Kerπp∗ via the derivative of lp : G…
Obstructions to homotopy equivalences
Reduced Weighted Complete Intersection and Derivations
Abstract Let A = F [ x 1 ,…, x n ]/( f 1 ,…, f n ) be a zero-dimensional weighted complete intersection (char  F =0). We prove a general result on the (homogeneous) derivations of A . In particular…
Finiteness in the minimal models of Sullivan
Let X be a 1-connected topological space such that the vector spaces I7I*(X) 0 Q and H*(X; Q) are finite dimensional. Then H*(X; Q) satisfies Poincare duality. Set Xr, = E(I)Pdim rlp(X) 0 Q and X, =…
Symmetric Bilinear Forms
I. Basic Concepts.- II. Symmetric Inner Product Spaces over Z.- III. Inner Product Spaces over a Field.- IV. Discrete Valuations and Dedekind Domains.- V. Some Examples.- Appendix 1. Quadratic…
Linear Algebraic Groups
We give a summary, without proofs, of basic properties of linear algebraic groups, with particular emphasis on reductive algebraic groups.
Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians
© Annales de l’institut Fourier, 1987, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions…
Contributions of rational homotopy theory to global problems in geometry
© Publications mathématiques de l’I.H.É.S., 1982, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
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