ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG a Matthias HAMMERL. On a new normalization for tractor covariant derivatives. Journal of the European Mathematical Society. Springer, 2012, roč. 14, č. 6, s. 1859-1883. ISSN 1435-9855. Dostupné z: https://dx.doi.org/10.4171/JEMS/349. |
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@article{1091238, author = {Šilhan, Josef and Souček, Vladimír and Somberg, Petr and Hammerl, Matthias}, article_number = {6}, doi = {http://dx.doi.org/10.4171/JEMS/349}, keywords = {Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry}, language = {eng}, issn = {1435-9855}, journal = {Journal of the European Mathematical Society}, title = {On a new normalization for tractor covariant derivatives}, url = {http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5}, volume = {14}, year = {2012} }
TY - JOUR ID - 1091238 AU - Šilhan, Josef - Souček, Vladimír - Somberg, Petr - Hammerl, Matthias PY - 2012 TI - On a new normalization for tractor covariant derivatives JF - Journal of the European Mathematical Society VL - 14 IS - 6 SP - 1859-1883 EP - 1859-1883 PB - Springer SN - 14359855 KW - Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry UR - http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5 L2 - http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5 N2 - 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. ER -
ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG a Matthias HAMMERL. On a new normalization for tractor covariant derivatives. \textit{Journal of the European Mathematical Society}. Springer, 2012, roč.~14, č.~6, s.~1859-1883. ISSN~1435-9855. Dostupné z: https://dx.doi.org/10.4171/JEMS/349.
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