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Commuting linear operators and algebraic decompositions

Rod A. Gover, Josef Šilhan (2007)

Archivum Mathematicum

For commuting linear operators P 0 , P 1 , , P we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition P = P 0 P 1 P in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem P u = f reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential...

Conformal curvature for the normal bundle of a conformal foliation

Angel Montesinos (1982)

Annales de l'institut Fourier

It is proved that the normal bundle of a distribution 𝒱 on a riemannian manifold admits a conformal curvature C if and only if 𝒱 is a conformal foliation. Then is conformally flat if and only if C vanishes. Also, the Pontrjagin classes of can be expressed in terms of C .

Conformal vector fields on Finsler manifolds

József Szilasi, Anna Tóth (2011)

Communications in Mathematics

Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection (‘pull-back formalism’), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Second, we deduce consequences on vector fields on the underlying manifold of a Finsler structure having one or two of the mentioned geometric properties.

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