Titlebook: Cartan Geometries and their Symmetries; A Lie Algebroid Appr Mike Crampin,David Saunders Book 2016 Atlantis Press and the author(s) 2016 Ca

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Infinitesimal Cartan Geometries on ,,examples (affine, projective, Riemannian and conformal geometries) all have realisations of this form, as indeed we have seen already in the affine and Riemannian cases. In the first four sections of this chapter we discuss each of these specific cases in turn, while in the final section we develop the general theory of such geometries.

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Conformal Geometry: The Full Version,g bundle will be spheres rather than projective spaces. In this chapter we shall explain how the action of a suitable group gives rise to such a sphere as a homogeneous space, and how the corresponding Cartan geometry can be constructed.

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Groupoids of Fibre Morphisms,onsider diffeomorphisms from one fibre to another that respect the group action in a suitable sense. Whereas the maps from a single fibre . satisfying such a condition will form a group, this will obviously not be the case when we consider maps with different domains and codomains: we will obtain, i

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Infinitesimal Cartan Geometries on ,,s of ., and therefore realise . as vector fields tangent to fibres, forming a representation of . on each fibre. There is then an interesting class of examples in which . and . consists of vector fields on the fibres whose coefficients are polynomial in the canonical fibre coordinates. The standard

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Developments and Geodesics,a Cartan geometry can be rolled, along a curve in it, on a fibre of . without slipping or twisting; the fibre of . can of course be considered as representative of the standard homogeneous-space fibre .. In suitable circumstances the same notion, of development, can be employed to define a geodesic

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Cartan Geometries and their Symmetries978-94-6239-192-5Series ISSN 2214-0700 Series E-ISSN 2214-0719