Abstract
The bundle of volume forms on a manifold is examined in terms of the affine connection defined by T. Y. Thomas. The choice of a particular affine connection in the projective class corresponds to the choice of an horizontal distribution on this bundle. The geometric properties of the horizontal distributions are studied. Special lifts of vector fields and covariant tensor fields are examined as well as lifts of metric connections.
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Dhooghe, P.F., Van Vlierden, A. Projective geometry on the bundle of volume forms. J Geom 62, 66–83 (1998). https://doi.org/10.1007/BF01237601
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DOI: https://doi.org/10.1007/BF01237601