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handle: 11584/94889
We introduce a new geometric structure on differentiable manifolds. A \textit{Contact} \textit{Pair}on a manifold $M$ is a pair $(��,��) $ of Pfaffian forms of constant classes $2k+1$ and $2h+1$ respectively such that $��\wedge d��^{k}\wedge��\wedge d��^{h}$ is a volume form. Both forms have a characteristic foliation whose leaves are contact manifolds. These foliations are transverse and complementary. Further differential objects are associated to Contact Pairs: two commuting Reeb vector fields, Legendrian curves on $M$ and two Lie brackets on $\mathcal{C}^{\infty}(M) $. We give a local model and several existence theorems on nilpotent Lie groups, nilmanifolds, bundles over the circle and principal torus bundles.
15 pages
Mathematics - Differential Geometry, Symplectic and contact topology in high or arbitrary dimension, 53D10, contact geometry, Reeb vector field, invariant forms, Differential Geometry (math.DG), Contact geometry, complementary foliations, FOS: Mathematics, Contact manifolds (general theory), 53D10; 57R17, 57R17
Mathematics - Differential Geometry, Symplectic and contact topology in high or arbitrary dimension, 53D10, contact geometry, Reeb vector field, invariant forms, Differential Geometry (math.DG), Contact geometry, complementary foliations, FOS: Mathematics, Contact manifolds (general theory), 53D10; 57R17, 57R17
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 19 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |