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The almost Einstein operator for \((2,3,5)\) distributions. (English) Zbl 1449.53033
A \((2,3,5)\) distribution on a 5-manifold is a \((2,3)\)-plane distribution which can be viewed as maximally non-integrable. This distribution induces a conformal structure of signature \((2,3)\). In the paper the corresponding tractor calculus is developed. The paper is motivated by the question whether the conformal structure contains an Einstein metric.

MSC:
53C18 Conformal structures on manifolds
53A40 Other special differential geometries
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
58A30 Vector distributions (subbundles of the tangent bundles)
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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