Abstract
This is the second in a series of articles on a natural modification of the normal tractor connection on parabolic geometries, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short review of the general procedure developed in Hammerl et al. (preprint) and then compute the prolongation covariant derivatives for a number of interesting examples in projective, conformal, and Grassmannian geometries.
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Hammerl, M., Somberg, P., Souček, V. et al. Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry. Ann Glob Anal Geom 42, 121–145 (2012). https://doi.org/10.1007/s10455-011-9306-9
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DOI: https://doi.org/10.1007/s10455-011-9306-9
Keywords
- Parabolic geometry
- Prolongation of invariant PDE’s
- BGG sequence
- Tractor covariant derivatives
- Projective geometry
- Conformal geometry
- Grassmannian geometry