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THE ALMOST EINSTEIN OPERATOR FOR (2, 3, 5) DISTRIBUTIONS.
- Source :
-
Archivum Mathematicum . 2017, Vol. 53 Issue 5, p347-370. 24p. - Publication Year :
- 2017
-
Abstract
- For the geometry of oriented (2, 3, 5) distributions (M,D), which correspond to regular, normal parabolic geometries of type (G2, P) for a particular parabolic subgroup P < G2, we develop the corresponding tractor calculus and use it to analyze the first BGG operator ⴱ0 associated to the 7-dimensional irreducible representation of G2. 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 are automatically normal, yielding a geometric interpretation of ker ⴱ0: For any (M,D), this kernel consists precisely of the almost Einstein scales of the Nurowski conformal structure on M that D determines. We apply our formula for ⴱ0 (1) to recover efficiently some known solutions, (2) to construct a distribution with root type [3, 1] with a nonzero solution, and (3) to show efficiently that the conformal holonomy of a particular (2, 3, 5) conformal structure is equal to G2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00448753
- Volume :
- 53
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Archivum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 127581899
- Full Text :
- https://doi.org/10.5817/AM2017-5-347