Tanaka structures (non holonomic G-structures) and Cartan connections

• Autoři: ALEKSEEVSKY Dmitry; DAVID Liana Rodica
• Rok publikování: 2015
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Journal of Geometry and Physics
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1016/j.geomphys.2015.01.018
• Obor: Obecná matematika
• Klíčová slova: Tanaka structures; (normal) Cartan connections; Parabolic geometry; (prolongation of) G-structures
• Popis: Let h = h(-k) circle plus ... circle plus h(1) (k > 0, l >= 0) be a finite dimensional graded Lie algebra, with a Euclidean metric <., .> adapted to the gradation. The metric <., .> is called admissible if the codifferentials partial derivative*: Ck+1 (h(-), j) -> C-k(h(-), h) (k >= 0) are Q-invariant (Lie(Q) = h(0) circle plus h(+)). We find necessary and sufficient conditions for a Euclidean metric, adapted to the gradation, to be admissible, and we develop a theory of normal Cartan connections, when these conditions are satisfied. We show how the treatment from Cap and Slovak (2009), about normal Cartan connections of semisimple type, fits into our theory. We also consider in detail the case when h := t*(g) is the cotangent Lie algebra of a non-positively graded Lie algebra g. (C) 2015 Elsevier B.V. All rights reserved.

Související projekty

• Algebraické metody v geometrii s potenciálem k aplikacím