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We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on $T^{2}$ which can be extended on a neighbourhood of $T^{2}$ into a projectively Anosov flow so that $T^{2}$ is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on $T^{3}$ . In this case, the only flows on $T^{2}$ which extend to $T^{3}$ ...

Prolongation of vector fields to jet bundles

Kolář, Ivan, Slovák, Jan (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation $J^{r} Y$ are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.

Prolongationally Stable Transformation Groups.

Ronald A. Knight (1978)

Mathematische Zeitschrift

Prolongement des champs de vecteurs à des variétés de points proches

Eugène Okassa (1986/1987)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Prolongement des homotopies, $Q$ -variétés et cycles tangents

Gaël Meigniez (1997)

Annales de l'institut Fourier

Nous montrons que le prolongement des homotopies, propriété de certains feuilletages étudiée par Godbillon, équivaut à la réunion de trois conditions indépendantes : la condition $Q$ de Barre, qui est transverse ; la trivialité des cycles évanouissants de toutes dimensions, et la trivialité des cycles apparents de toutes dimensions. On établit que pour les feuilletages riemanniens et pour les feuilletages géodésibles, la propriété $Q$ équivaut à l’absence d’holonomie. Ces résultats sont ensuite appliqués...

Proper actions and a compactness condition.

Lipsman, Ronald L. (1995)

Journal of Lie Theory

Proper homotopies in $l_{2}$ -manifolds

R. D. Anderson (1971)

Compositio Mathematica

Properly homotopic nontrivial planes are isotopic

Bobby Winters (1995)

Fundamenta Mathematicae

It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to $ℝ^{3}$ are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.

Properties of product preserving functors

Gancarzewicz, Jacek, Mikulski, Włodzimierz, Pogoda, Zdzisław (1994)

Proceedings of the Winter School "Geometry and Physics"

A product preserving functor is a covariant functor $ℱ$ from the category of all manifolds and smooth mappings into the category of fibered manifolds satisfying a list of axioms the main of which is product preserving: $ℱ (M_{1} \times M_{2}) = ℱ (M_{1}) \times ℱ (M_{2})$ . It is known that any product preserving functor $ℱ$ is equivalent to a Weil functor $T^{A}$ . Here $T^{A} (M)$ is the set of equivalence classes of smooth maps $ϕ : ℝ^{n} \to M$ and $ϕ, ϕ^{'}$ are equivalent if and only if for every smooth function $f : M \to ℝ$ the formal Taylor series at 0 of $f \circ ϕ$ and $f \circ ϕ^{'}$ are equal in $A = ℝ [[x_{1}, \dots, x_{n}]] / 𝔞$ . In this paper all...

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Profondeur homotopique et conjecture de grothendieck

Projections of knots

Projective and Hilbert modules over group algebras, and finitely dominated spaces.

Projective Connections in CR Geometry.

Projective limits of Banach vector bundles.

Projective Planes in Irreducible 3-Manifolds.

Projective varieties invariant by one-dimensional foliations.

Projective varieties with non-residually finite fundamental group

Projectively Anosov flows with differentiable (un)stable foliations