Path geometries admit parametrized distinguished connections that enable elementary tractor calculus plus a unique subclass of Weyl structures linked to refined de Rham complexes.
Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structures
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abstract
We study the standard tractor bundle and the standard cotractor bundle of an almost Grassmann structure: We provide explicit formulae for their splitting operators, first BGG operators as well as prolongation connections. We characterize parallel tractors and cotractors as well as the solutions of the BGG operators in standard geometric terms. Moreover, we describe the geometry canonically endowed on the zero locus of a solution of the first BGG operators.
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UNVERDICTED 2representative citing papers
Defines a normal Fefferman-type construction from (n+1)-dimensional path geometries to almost Grassmannian structures of type (2,n+1) with characterizations via parallel tractors and Weyl connections, plus a related non-normal construction from type (2,n) structures.
citing papers explorer
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Weyl structures for path geometries
Path geometries admit parametrized distinguished connections that enable elementary tractor calculus plus a unique subclass of Weyl structures linked to refined de Rham complexes.
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Two Fefferman-type constructions involving almost Grassmann structures and path geometries
Defines a normal Fefferman-type construction from (n+1)-dimensional path geometries to almost Grassmannian structures of type (2,n+1) with characterizations via parallel tractors and Weyl connections, plus a related non-normal construction from type (2,n) structures.