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The constructions of general connections on second jet prolongation

Mariusz Plaszczyk (2014)

Annales UMCS, Mathematica

We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M

The contact system for A -jet manifolds

R. J. Alonso-Blanco, J. Muñoz-Díaz (2004)

Archivum Mathematicum

Jets of a manifold M can be described as ideals of 𝒞 ( M ) . This way, all the usual processes on jets can be directly referred to that ring. By using this fact, we give a very simple construction of the contact system on jet spaces. The same way, we also define the contact system for the recently considered A -jet spaces, where A is a Weil algebra. We will need to introduce the concept of derived algebra.

The contact system on the ( m , ) -jet spaces

J. Muñoz, F. J. Muriel, Josemar Rodríguez (2001)

Archivum Mathematicum

This paper is a continuation of [MMR:98], where we give a construction of the canonical Pfaff system Ω ( M m ) on the space of ( m , ) -velocities of a smooth manifold M . Here we show that the characteristic system of Ω ( M m ) agrees with the Lie algebra of Aut ( m ) , the structure group of the principal fibre bundle M ˇ m J m ( M ) , hence it is projectable to an irreducible contact system on the space of ( m , ) -jets ( = -th order contact elements of dimension m ) of M . Furthermore, we translate to the language of Weil bundles the structure form...

The CR Yamabe conjecture the case n = 1

Najoua Gamara (2001)

Journal of the European Mathematical Society

Let ( M , θ ) be a compact CR manifold of dimension 2 n + 1 with a contact form θ , and L = ( 2 + 2 / n ) Δ b + R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form θ ˜ on M conformal to θ which has a constant Webster curvature. This problem is equivalent to the existence of a function u such that L u = u 1 + 2 / n , u > 0 on M . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where n 2 and ( M , θ ) is not locally CR equivalent to the sphere S 2 n + 1 of 𝐂 n . In a join work with R. Yacoub, the CR Yamabe problem...

The diffeomorphism group of a Lie foliation

Gilbert Hector, Enrique Macías-Virgós, Antonio Sotelo-Armesto (2011)

Annales de l’institut Fourier

We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus T n , n 2 . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are ± Id and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for T 2 , P. Iglesias and...

Currently displaying 61 – 80 of 488