Geodesic
The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 21-38

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We define a conformally connected space with arbitrary signature of angular metric and present basic formulas and classes of such spaces. We obtain the decomposition of the main tensor of a conformally connected torsion-free space into irreducible gauge-invariant summands and prove the following new property of the Weyl tensor: all affine connections obtained from the Levi-Civita connection via the normalization transformation have the same conformal Weyl tensor. We describe all conformal torsion-free connections on hypersurfaces of a projective space and give some examples. We construct a global conformal connection on a hyperquadric of the projective space.
Keywords: conformally connected space, Weyl tensor of conformal curvature, angular metric, gauge transformations, curvature
Mots-clés : torsion. 
@article{VNGU_2017_17_2_a2,
     author = {L. N. Krivonosov and V. A. Luk'yanov},
     title = {The structure of the main tensor of conformally connected torsion-free space. {Conformal} connections on hypersurfaces of projective space},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {21--38},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a2/}
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L. N. Krivonosov; V. A. Luk'yanov. The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 21-38. http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a2/