Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
natural operator; product preserving bundle functor; Weil algebra; Poisson structure
natural operator; product preserving bundle functor; Weil algebra; Poisson structure
Summary:
We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.
References:
[1] J. Dębecki: Linear liftings of skew-symmetric tensor fields to Weil bundles. Czechoslovak Math. J 55(130) (2005), 809-816. DOI 10.1007/s10587-005-0067-0 | MR 2153104
[2] D. J. Eck: Product-preserving functors on smooth manifolds. J. Pure Appl. Algebra 42 (1986), 133–140. DOI 10.1016/0022-4049(86)90076-9 | MR 0857563 | Zbl 0615.57019
[3] J. Gancarzewicz, W. Mikulski, and Z. Pogoda: Lifts of some tensor fields and connections to product preserving functors. Nagoya Math. J. 135 (1994), 1–41. DOI 10.1017/S0027763000004931 | MR 1295815
[4] J. Grabowski, P. Urbański: Tangent lifts of Poisson and related structures. J. Phys. A, Math. Gen. 28 (1995), 6743–6777. DOI 10.1088/0305-4470/28/23/024 | MR 1381143
[5] G. Kainz, P. W. Michor: Natural transformations in differential geometry. Czechoslovak Mat. J. 37(112) (1987), 584–607. MR 0913992
[6] I. Kolář: On the natural operators on vector fields. Ann. Global Anal. Geom. 6 (1988), 109–117. DOI 10.1007/BF00133034 | MR 0982760
[7] I. Kolář: Jet-like approach to Weil bundles. Seminar Lecture Notes, Masaryk University, Brno, 2001.
[8] I. Kolář, P. W. Michor, J. Slovák: Natural Operations in Differential Geometry. Springer-Verlag, Berlin, 1993. MR 1202431
[9] O. O. Luciano: Categories of multiplicative functors and Weil’s infinitely near points. Nagoya Math. J. 109 (1988), 69–89. DOI 10.1017/S0027763000002774 | MR 0931952 | Zbl 0661.58007
[10] W. M. Mikulski: The linear natural operators lifting $2$-vector fields to some Weil bundles. Note Mat. 19 (1999), 213–217. MR 1816875 | Zbl 1008.58004
[11] I. Vaisman: Lectures on the Geometry of Poisson Manifolds. Birkhäuser-Verlag, Basel, 1994. MR 1269545 | Zbl 0810.53019
Search
Partner of
