Si annunciano alcuni risultati relativi agli automorfismi infinitesimali quaternionali, in particolare una formula di tipo Bott che lega i loro zeri con i numeri simplettici di Pontrjagin.
We construct the CR invariant canonical contact form on scalar positive spherical CR manifold , which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold , where is a convex cocompact subgroup of and is the discontinuity domain of . This contact form can be used to prove that is scalar positive (respectively, scalar negative, or scalar vanishing) if and...
Let M be a smooth manifold of dimension m>0, and denote by the canonical Nijenhuis tensor on TM. Let Π be a Poisson bivector on M and the complete lift of Π on TM. In a previous paper, we have shown that is a Poisson-Nijenhuis manifold. Recently, the higher order tangent lifts of Poisson manifolds from M to have been studied and some properties were given. Furthermore, the canonical Nijenhuis tensors on are described by A. Cabras and I. Kolář [Arch. Math. (Brno) 38 (2002), 243-257],...
We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr0 (R;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TrM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σrk=0 αkω(k) for all real numbers αk with αr ≠ 0, where ω(k) is the (k)-lift (in the sense of A. Morimoto) of ω to TrM.
The purpose of this paper is to define transversal Cartan connection of Finsler foliation and to prove its existence and uniqueness.