2009/05/04 by Oana Constantinescu, Constantinescu, Oana, Mircea Crâşmăreanu +2
Engineering · Mathematics · Physics and Astronomy · #53C05 #53C12 #53C60 #Differential Geometry (math.DG) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C05 #msc:53C12 #msc:53C60
paper · pdf · doi:10.48550/arxiv.0905.0362
15 pages
arxiv created 2009/05/04 · openalex publication_date 2009/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to study from the point of view of linear connections the data (M,D,g,W), with M a smooth (n+p) dimensional real manifold, (D,g) a ndimensional semi-Riemannian distributionon M, G the conformal structure generated by g and W a Weyl substructure: a map W: G→ Ω1(M) such that W(g)=W(g)-du, g=eug;u∈ C∞(M). Compatible linear connections are introduced as a natural extension of similar notions from Riemannian geometry and such a connection is unique if a symmetry condition is imposed. In the foliated case the local expression of this unique connection is obtained. The notion of Vranceanu connection is introduced for a pair (Weyl structure, distribution) and it is computed for the tangent bundle of Finsler spaces, particularly Riemannian, choosing as distribution the vertical bundle of tangent bundle projection and as 1-form the Cartan form.