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In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.

Riemannian $L^{p}$ structures and $K$ -homology. (Structures riemanniennes $L^{p}$ et $K$ -homologie.)

Hilsum, Michel (1999)

Annals of Mathematics. Second Series

Riemannian manifolds not quasi-isometric to leaves in codimension one foliations

Paul A. Schweitzer (2011)

Annales de l’institut Fourier

Every open manifold $L$ of dimension greater than one has complete Riemannian metrics $g$ with bounded geometry such that $(L, g)$ is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of $(L, g)$ suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of $(L, g)$ that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential...

Riemannian manifolds with many Killing vector fields

Ann Stehney, Richard Millman (1980)

Fundamenta Mathematicae

Riemann-Roch theorem after D. Toledo and Y.-L. Tong

Schechtman, V. V. (1989)

Proceedings of the Winter School "Geometry and Physics"

Riemann-Roch theorem and Lie algebra cohomology

Feigin, B. L., Tsygan, B. L. (1989)

Proceedings of the Winter School "Geometry and Physics"

Rigid sets in manifolds

David G. Wright (1986)

Banach Center Publications

Rigid versus non-rigid cyclic actions.

K.-H. Dovermann, M. Masuda (1989)

Commentarii mathematici Helvetici

Rigidity and crystallographic groups, I.

Frank Conolly, Tadeusz Kozniewski (1990)

Inventiones mathematicae

Rigidity and gluing for Morse and Novikov complexes

Octav Cornea, Andrew Ranicki (2003)

Journal of the European Mathematical Society

We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold $(M, ω)$ with $c_{1} {|_{π_{2} (M)} = [ω] |}_{π_{2} (M)} = 0$ . The rigidity results for these complexes show that the complex of a fixed generic function/hamiltonian is a retract of the Morse (respectively Novikov or Floer) complex of any other sufficiently $C^{0}$ close generic function/hamiltonian....

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Displaying 121 – 140 of 152

Revêtements «spinoriels» du groupe symplectique et indices de Maslov

Ribbon Concordance of Knots in the 3-Sphere.

Ribbon knots of 1-fusion, the Jones polynomial, and the Casson-Walker invariant.

Riemann surfaces and spin structures

Riemannian foliations on Manifolds with non-negative curvature.

Riemannian foliations with parallel or harmonic basic forms

Riemannian $L^{p}$ structures and $K$ -homology. (Structures riemanniennes $L^{p}$ et $K$ -homologie.)

Riemannian manifolds not quasi-isometric to leaves in codimension one foliations

Riemannian manifolds with many Killing vector fields

Riemann-Roch theorem after D. Toledo and Y.-L. Tong

Riemann-Roch theorem and Lie algebra cohomology

Rigid sets in manifolds

Rigid versus non-rigid cyclic actions.

Rigidity and crystallographic groups, I.

Rigidity and gluing for Morse and Novikov complexes

Rigidity and the lower bound Theorem l.

Rigidity of certain finite group actions on the complex projective plane.

Rigidity of cusps in deformations of hyperbolic 3-orbifolds.

Rigidity of Furstenberg entropy for semisimple Lie group actions

Rigidity of hypersurfaces in complex projective space

Currently displaying 121 – 140 of 152