Geodesic
Parabolic Conformally Symplectic Structures. III: Invariant Differential Operators and Complexes
Documenta mathematica, Tome 24 (2019), pp. 2203-2240.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

This is the last part of a series of articles on a family of geometric structures (PACS-structures) which all have an underlying almost conformally symplectic structure. While the first part of the series was devoted to the general study of these structures, the second part focused on the case that the underlying structure is conformally symplectic (PCS-structures). In that case, we obtained a close relation to parabolic contact structures via a concept of parabolic contactification. It was also shown that special symplectic connections (and thus all connections of exotic symplectic holonomy) arise as the canonical connection of such a structure. \par In this last part, we use parabolic contactifications and constructions related to Bernstein-Gelfand-Gelfand (BGG) sequences for parabolic contact structures, to construct sequences of differential operators naturally associated to a PCS-structure. In particular, this gives rise to a large family of complexes of differential operators associated to a special symplectic connection. In some cases, large families of complexes for more general instances of PCS-structures are obtained.
Classification : 53D05, 53D10, 53C15, 58J10, 53C10, 53C55, 58A10
Keywords: parabolic geometry, conformally symplectic structure, invariant differential operator, differential complex, BGG sequence 
@article{DOCMA_2019__24__a11,
     author = {\v{C}ap, Andreas and Sala\v{c}, Tom\'a\v{s}},
     title = {Parabolic {Conformally} {Symplectic} {Structures.} {III:} {Invariant} {Differential} {Operators} and {Complexes}},
     journal = {Documenta mathematica},
     pages = {2203--2240},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a11/}
}
TY  - JOUR
AU  - Čap, Andreas
AU  - Salač, Tomáš
TI  - Parabolic Conformally Symplectic Structures. III: Invariant Differential Operators and Complexes
JO  - Documenta mathematica
PY  - 2019
SP  - 2203
EP  - 2240
VL  - 24
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a11/
LA  - en
ID  - DOCMA_2019__24__a11
ER  - 
%0 Journal Article
%A Čap, Andreas
%A Salač, Tomáš
%T Parabolic Conformally Symplectic Structures. III: Invariant Differential Operators and Complexes
%J Documenta mathematica
%D 2019
%P 2203-2240
%V 24
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a11/
%G en
%F DOCMA_2019__24__a11
Čap, Andreas; Salač, Tomáš. Parabolic Conformally Symplectic Structures. III: Invariant Differential Operators and Complexes. Documenta mathematica, Tome 24 (2019), pp. 2203-2240. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a11/