Isometry-invariant geodesics and nonpositive derivations of the cohomology

  title={Isometry-invariant geodesics and nonpositive derivations of the cohomology},
  author={Stefan Papadima and Laurentiu Paunescu},
  journal={Journal of Differential Geometry},
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… 
Closed manifolds coming from Artinian complete intersections
We reformulate the integrality property of the Poincare inner product in the middle dimension, for an arbitrary Poincare Q-algebra, in classical terms (discriminant and local invariants). When the
Non-closed isometry-invariant geodesics
Let c be a non-closed and bounded geodesic in a complete Riemannian manifold M. Assume that c is invariant under an isometry A of M and that c is not contained in the set of fixed points of A. We
We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré Q-algebra, in classical terms (discriminant and local invariants). When the
Splitting lemmas for the Finsler energy functional on the space of H1‐curves
We establish the splitting lemmas (or generalized Morse lemmas) for the energy functionals of Finsler metrics on the natural Hilbert manifolds of H1 ‐curves around a critical point or a critical R1
Papadima volume
S, tefan Papadima was born in Bucharest, Romania on 7 March 1953, in a family of literary-oriented intellectuals. His father, Ovidiu, was a distinguished literary critic, while his mother, S,
Non-existence of negative weight derivations on positively graded Artinian algebras
It is shown that R equals double-struck upper C left-bracket x 1 comma x 2 comma ellipsis comma x Subscript n Baseline right-BRacket slash left-parenthesis f 1 comma ellipis comma f Subscript m Baseline left-parentshesis is equal to R.


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
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Contributions of rational homotopy theory to global problems in geometry
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