Geodesic
Projective equivalence and manifolds with equiaffine connection
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 47-54.

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In this paper, we prove that all manifolds with affine or projective connection are globally projectively equivalent to some manifolds with equiaffine connection (equiaffine manifold). 
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I. Hinterleitner; J. Mikeš. Projective equivalence and manifolds with equiaffine connection. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 47-54. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a3/

[1] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., Shirokov A. P., “Differentsialno-geometricheskie struktury na mnogoobraziyakh”, Itogi nauki i tekhn. Ser. Probl. geom. Tr. geom. sem., 9, 1979, 5–246

[2] Mikesh I., “Geodezicheskie otobrazheniya affinnosvyaznykh i rimanovykh prostranstv”, Itogi nauki i tekhn. Ser. Sovrem. mat. i eë pril., 11, 2002, 121–162 | MR | Zbl

[3] Norden A. P., Prostranstva affinnoi svyaznosti, Nauka, M., 1976 | MR | Zbl

[4] Petrov A. Z., Novye metody v teorii otnositelnosti, Nauka, M., 1965

[5] Sinyukov N. S., Geodezicheskie otobrazheniya rimanovykh prostranstv, Nauka, M., 1979 | MR | Zbl

[6] Skhouten I. A., Stroik D. Dzh., Vvedenie v novye metody differentsialnoi geometrii, v. I, Gostekhizdat, M.–L., 1939; т. II, ИЛ, М., 1949

[7] Eastwood M., Matveev V. S., “Metric connections in projective differential geometry”, Symmetries and Overdetermined Systems of Partial Differential Equations (Minneapolis, MN, 2006), IMA Vol. Math. Appl., 144, Springer, New York, 2007, 339–351 | DOI | MR

[8] Eisenhart L. P., Non-Riemannian geometry, Amer. Math. Soc. Colloq. Publ., 8, Amer. Math. Soc., 2000 | MR

[9] Hall G. S., Lonie D. P., “Projective equivalence of Einstein spaces in general relativity”, Classical Quantum Gravity, 26:12 (2009), 125009, 10 pp. | DOI | MR | Zbl

[10] Levi-Civita T., “Sulle transformazioni delle equazioni dinamiche”, Ann. Mat. Milano, 24:2 (1886)

[11] Mikeš J., Berezovski V., “Geodesic mappings of affine-connected spaces onto Riemannian spaces”, Colloq. Math. Soc. Janos Bolyai, 56 (1989), 491–494 | MR

[12] Mikeš J., Hinterleitner I., On geodesic mappings of manifolds with affine connection, 2009, arXiv: math.DG/0905.1839v2 | MR

[13] Mikeš J., Hinterleitner I., Kiosak V., “On the theory of geodesic mappings of Einstein spaces and their generalizations”, Acta Phys. Debrecena, 861 (2006), 428–435

[14] Mikeš J., Kiosak V., Vanžurová A., Geodesic Mappings of Manifolds with Affine Connection, Palacký Univ. Press, Olomouc, 2008 | MR | Zbl

[15] Thomas T. Y., “On the projective and equi-projective geometries of paths”, Proc. Nat. Acad. Sci. U.S.A., 11 (1925), 198–203 | Zbl

[16] Weyl H., “Zur Infinitesimalgeometrie Einordnung der Projectiven und der Konformen Auffassung”, Göttinger Nachr., 1921, 99–112 | Zbl