A nonstandard operator for almost Grassmannian geometries with a torsion

Aleš Návrat

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arXiv · 1509.09084

A nonstandard operator for almost Grassmannian geometries with a torsion

Aleš Návrat

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Abstract

A nonstandard invariant fourth order operator acting on functions on a manifold equipped with an almost Grassmannian structure with an arbitrary trorsion is found by means of the curved translation principle. This operator can be viewed as a Grassmannian analogue of the Paneitz operator well known from conformal geometry. It is obtained by translating a Grassmannian analogue of the Laplace operator to a certain tractor bundle with a specific tractor connection, which is not normal in general.

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Aleš Návrat. 2015-09-30. A nonstandard operator for almost Grassmannian geometries with a torsion. https://arxiv.org/abs/1509.09084

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