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A construction of a connection on G Y Y from a connection on Y M by means of classical linear connections on M and Y

Włodzimierz M. Mikulski (2005)

Commentationes Mathematicae Universitatis Carolinae

Let G be a bundle functor of order ( r , s , q ) , s r q , on the category m , n of ( m , n ) -dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection Γ on an m , n -object Y M we construct a general connection 𝒢 ( Γ , λ , Λ ) on G Y Y be means of an auxiliary q -th order linear connection λ on M and an s -th order linear connection Λ on Y . Then we construct a general connection 𝒢 ( Γ , 1 , 2 ) on G Y Y by means of auxiliary classical linear connections 1 on M and 2 on Y . In the case G = J 1 we determine all general connections 𝒟 ( Γ , ) on J 1 Y Y from...

A convex Darboux theorem

Pierre-André Chiappori, Ivar Ekeland (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A description of derivations of the algebra of symmetric tensors

A. Heydari, N. Boroojerdian, E. Peyghan (2006)

Archivum Mathematicum

In this paper the symmetric differential and symmetric Lie derivative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified. We also define a Frölicher-Nijenhuis bracket for vector valued symmetric tensors.

A generalization of the exterior product of differential forms combining Hom-valued forms

Christian Gross (1997)

Commentationes Mathematicae Universitatis Carolinae

This article deals with vector valued differential forms on C -manifolds. As a generalization of the exterior product, we introduce an operator that combines Hom ( s ( W ) , Z ) -valued forms with Hom ( s ( V ) , W ) -valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.

A generalization of Thom’s transversality theorem

Lukáš Vokřínek (2008)

Archivum Mathematicum

We prove a generalization of Thom’s transversality theorem. It gives conditions under which the jet map f * | Y : Y J r ( D , M ) J r ( D , N ) is generically (for f : M N ) transverse to a submanifold Z J r ( D , N ) . We apply this to study transversality properties of a restriction of a fixed map g : M P to the preimage ( j s f ) - 1 ( A ) of a submanifold A J s ( M , N ) in terms of transversality properties of the original map f . Our main result is that for a reasonable class of submanifolds A and a generic map f the restriction g | ( j s f ) - 1 ( A ) is also generic. We also present an example of A where the...

A generalized sharp Whitney theorem for jets.

Charles Fefferman (2005)

Revista Matemática Iberoamericana

Suppose that, for each point x in a given subset E ⊂ Rn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".

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