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Tensor approach to multidimensional webs

Alena Vanžurová (1998)

Mathematica Bohemica

An anholonomic ( n + 1 ) -web of dimension r is considered as an ( n + 1 ) -tuple of r -dimensional distributions in general position. We investigate a family of ( 1 , 1 ) -tensor fields (projectors and nilpotents associated with a web in a natural way) which will be used for characterization of all linear connections on a manifold preserving the given web.

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 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 asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries

Frank Müller (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.

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