English

A nonstandard operator for almost Grassmannian geometries with a torsion

Differential Geometry 2015-10-01 v1

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.

Keywords

Cite

@article{arxiv.1509.09084,
  title  = {A nonstandard operator for almost Grassmannian geometries with a torsion},
  author = {Aleš Návrat},
  journal= {arXiv preprint arXiv:1509.09084},
  year   = {2015}
}