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Tensor valued Colombeau functions on manifolds

M. Grosser (2010)

Banach Center Publications

Extending the construction of the algebra ^ ( M ) of scalar valued Colombeau functions on a smooth manifold M (cf. [4]), we present a suitable basic space for eventually obtaining tensor valued generalized functions on M, via the usual quotient construction. This basic space canonically contains the tensor valued distributions and permits a natural extension of the classical Lie derivative. Its members are smooth functions depending-via a third slot-on so-called transport operators, in addition to slots...

The affine approach to homogeneous geodesics in homogeneous Finsler spaces

Zdeněk Dušek (2018)

Archivum Mathematicum

In the recent paper [Yan, Z.: Existence of homogeneous geodesics on homogeneous Finsler spaces of odd dimension, Monatsh. Math. 182,1, 165–171 (2017)], it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. However, the proof contains a serious gap. The situation is a bit delicate, because the statement is correct. In the present paper, the incorrect part in this proof is indicated. Further, it is shown that homogeneous geodesics in homogeneous...

The almost Einstein operator for ( 2 , 3 , 5 ) distributions

Katja Sagerschnig, Travis Willse (2017)

Archivum Mathematicum

For the geometry of oriented ( 2 , 3 , 5 ) distributions ( M , ) , which correspond to regular, normal parabolic geometries of type ( G 2 , P ) for a particular parabolic subgroup P < G 2 , we develop the corresponding tractor calculus and use it to analyze the first BGG operator Θ 0 associated to the 7 -dimensional irreducible representation of G 2 . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...

The approximate symmetries of the vacuum Einstein equations

Tiller, Petr (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

The author reviews the theory of approximate infinitesimal symmetries of partial differential equations. Based on this and on Ibragimov's result on the general symmetries of the vacuum Einstein equation, he proposes a method to calculate approximate symmetries of the non-vacuum Einstein equation: the energy-momentum tensor is treated like a perturbation.

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