Abstract
We introduce a class of first order G-structures, each of which has an underlying almost conformally symplectic structure.
There is one such structure for each real simple Lie algebra which is not of type
Funding source: Austrian Science Fund
Award Identifier / Grant number: P23244-N13
Award Identifier / Grant number: P27072-N25
Funding statement: Support by projects P23244-N13 (both authors) and P27072-N25 (first author) of the Austrian Science Fund (FWF) is gratefully acknowledged.
References
[1] R. L. Bryant, Bochner–Kähler metrics, J. Amer. Math. Soc. 14 (2001), no. 3, 623–715. 10.1090/S0894-0347-01-00366-6Search in Google Scholar
[2] M. Cahen and L. J. Schwachhöfer, Special symplectic connections, J. Differential Geom. 83 (2009), no. 2, 229–271. 10.4310/jdg/1261495331Search in Google Scholar
[3] D. M. J. Calderbank and T. Diemer, Differential invariants and curved Bernstein–Gelfand–Gelfand sequences, J. Reine Angew. Math. 537 (2001), 67–103. 10.1515/crll.2001.059Search in Google Scholar
[4] A. Čap and T. Salač, Pushing down the Rumin complex to conformally symplectic quotients, Differential Geom. Appl. 35 (2014), 255–265. 10.1016/j.difgeo.2014.05.004Search in Google Scholar
[5] A. Čap and T. Salač, Parabolic conformally symplectic structures II; parabolic contactification, preprint (2016), https://arxiv.org/abs/1605.01897. 10.1007/s10231-017-0719-3Search in Google Scholar
[6] A. Čap and T. Salač, Parabolic conformally symplectic structures III; invariant differential operators and complexes, preprint (2017), https://arxiv.org/abs/1701.01306. Search in Google Scholar
[7] A. Čap and J. Slovák, Parabolic Geometries. I. Background and General Theory, Math. Surveys Monogr. 154, American Mathematical Society, Providence, 2009. 10.1090/surv/154Search in Google Scholar
[8] A. Čap and J. Slovák, and V. Souček, Bernstein–Gelfand–Gelfand sequences, Ann. of Math. (2) 154 (2001), no. 1, 97–113. 10.2307/3062111Search in Google Scholar
[9] M. Eastwood and H. Goldschmidt, Zero-energy fields on complex projective space, J. Differential Geom. 94 (2013), no. 1, 129–157. 10.4310/jdg/1361889063Search in Google Scholar
[10] M. Eastwood and J. Slovák, Conformally Fedosov manifolds, preprint (2012), https://arxiv.org/abs/1210.5597. 10.1016/j.aim.2019.04.004Search in Google Scholar
[11] A. Gray and L. M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. (4) 123 (1980), 35–58. 10.1007/BF01796539Search in Google Scholar
[12] B. Kostant, Lie algebra cohomology and the generalized Borel–Weil theorem, Ann. of Math. (2) 74 (1961), 329–387. 10.2307/1970237Search in Google Scholar
[13] S. Merkulov and L. Schwachhöfer, Classification of irreducible holonomies of torsion-free affine connections, Ann. of Math. (2) 150 (1999), no. 1, 77–149. 10.2307/121098Search in Google Scholar
[14] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, 1964. Search in Google Scholar
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