"1"^^ . "Journal of the European Mathematical Society" . "10.4171/JEMS/349" . . . "On a new normalization for tractor covariant derivatives"@en . "\u0160ilhan, Josef" . "On a new normalization for tractor covariant derivatives" . . . "Hammerl, Matthias" . . . "156164" . . . "25"^^ . "On a new normalization for tractor covariant derivatives"@en . "6" . . . "Somberg, Petr" . "http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5" . . "A regular normal parabolic geometry of type G/P on a manifold M gives rise to sequences $D_i$ of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative $\\nabla^\\omega$ on the corresponding tractor bundle V, where $\\omega$ is the normal Cartan connection. The first operator $D_0$ in the sequence is overdetermined and it is well known that $\\nabla^\\omega$ yields the prolongation of this operator in the homogeneous case M = G/P. Our first main result is the curved version of such a prolongation. This requires a new normalization of the tractor covariant derivative on V. Moreover, we obtain an analogue for higher operators $D_i$. In that case one needs to modify the exterior covariant derivative $d^{\\nabla^\\omega}$ by differential terms. Finally we illustrate these results with simple examples in projective, conformal and Grassmannian geometry. Our approach is based on standard BGG techniques."@en . "RIV/00216224:14310/12:00064347!RIV13-MSM-14310___" . "14310" . "000311877200005" . "Parabolic geometry - prolongation of invariant PDE\u2019s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry"@en . "CH - \u0160v\u00FDcarsk\u00E1 konfederace" . . . . . "A regular normal parabolic geometry of type G/P on a manifold M gives rise to sequences $D_i$ of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative $\\nabla^\\omega$ on the corresponding tractor bundle V, where $\\omega$ is the normal Cartan connection. The first operator $D_0$ in the sequence is overdetermined and it is well known that $\\nabla^\\omega$ yields the prolongation of this operator in the homogeneous case M = G/P. Our first main result is the curved version of such a prolongation. This requires a new normalization of the tractor covariant derivative on V. Moreover, we obtain an analogue for higher operators $D_i$. In that case one needs to modify the exterior covariant derivative $d^{\\nabla^\\omega}$ by differential terms. Finally we illustrate these results with simple examples in projective, conformal and Grassmannian geometry. Our approach is based on standard BGG techniques." . "[F02C45E039E5]" . "Sou\u010Dek, Vladim\u00EDr" . "P(LC505), Z(MSM0021620839)" . "RIV/00216224:14310/12:00064347" . "On a new normalization for tractor covariant derivatives" . "14" . "4"^^ . . "1435-9855" .