Weyl substructures and compatible linear connections

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dc.creatorConstantinescu, Oana
dc.creatorCrasmareanu, Mircea
dc.date2009-05-04
dc.date.accessioned2026-07-07T13:11:26Z
dc.date.available2026-07-07T13:11:26Z
dc.descriptionThe aim of this paper is to study from the point of view of linear connections the data $(M,\mathcal{D},g,W),$ with $M$ a smooth $(n+p)$ dimensional real manifold, $(\mathcal{D},g)$ a \textit{$n$}\textit{\emph{dimensional semi-Riemannian distribution}}\emph{}on $M,$ $\mathcal{G}$ the conformal structure generated by $g$ and $W$ a Weyl substructure: a map $W:$ $\mathcal{G}\to$ $Ω^{1}(M)$ such that $W(\overline{g})=W(g)-du,$ $\overline{g}=e^{u}g;u\in C^{\infty}(M)$. 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.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0905.0362
dc.identifierhttp://arxiv.org/abs/0905.0362
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229282
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C05; 53C12; 53C60
dc.titleWeyl substructures and compatible linear connections
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