Metric Affine Spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 146 (2018), pp. 89-102.

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This paper is a review of some directions of the study of special classes of metric affince spaces.
Keywords: metric, connection
Mots-clés : automorphism, Lie group.
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V. I. Panzhenskii; S. E. Stepanov; M. V. Sorokina. Metric Affine Spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 146 (2018), pp. 89-102. http://geodesic.mathdoc.fr/item/INTO_2018_146_a3/

[1] Baburova O. V., Frolov B. N., Matematicheskie osnovy sovremennoi teorii gravitatsii, MPGU, M., 2012

[2] Veil G., Prostranstvo. Vremya. Materiya, Editorial URSS, M., 2004

[3] Gordeeva I. A., “O nekotorykh klassakh prostranstv Veittsenbeka”, Izv. Penz. gos. ped. un-ta. Fiz.-mat. tekhn. nauki, 26:1 (2011), 70–75

[4] Panzhenskii V. I., “Maksimalno podvizhnye rimanovy prostranstva s krucheniem”, Mat. zametki, 85:5 (2009), 754–757 | DOI | MR | Zbl

[5] Panzhenskii V. I., “Finslerovo obobschenie struktury Rimana—Kartana”, Izv. Penz. gos. ped. un-ta. Fiz.-mat. tekhn. nauki, 26:1 (2011), 155–159

[6] Panzhenskii V. I., “Statsionarnaya model Vselennoi s krucheniem”, Teor. mat. fiz., 177:1 (2013), 151–162 | DOI

[7] Panzhenskii V. I., “Avtomorfizmy mnogoobrazii Rimana—Kartana”, Mat. zametki, 98:4 (2015), 544–556 | DOI | MR | Zbl

[8] Panzhenskii V. I., Surina O. P., “Finslerovo obobschenie metriki Tamma”, Teor. mat. fiz., 189:2 (2016), 186–197 | DOI | MR | Zbl

[9] Rylov A. A., “Svyaznosti Amari—Chentsova na logisticheskoi modeli”, Izv. Penz. gos. ped. un-ta. Fiz.-mat. tekhn. nauki, 26:1 (2011), 195–206

[10] Stepanov S. E., Gordeeva I. A., “Psevdokillingovy i psevdogarmonicheskie vektornye polya na mnogoobrazii Rimana—Kartana”, Mat. zametki, 87:2 (2010), 267–279 | DOI | Zbl

[11] Stepanov S. E., Stepanova E. S., Shandra I. G., “Sopryazhennye svyaznosti na statisticheskikh mnogoobraziyakh”, Izv. vuzov. Mat., 2007, no. 10, 90–98 | Zbl

[12] Stepanova E. S., Tsyganok I. I., “Sopryazhennoe Richchi-simmetricheskoe statisticheskoe mnogoobrazie”, Tez. dokl. Mezhdunar. konf. po differ. uravn. i dinamich. sist., Vladimir. gos. un-t, Vladimir, 2006, 207–208

[13] Stepanova E. S., Tsyganok I. I., “Statisticheskie mnogoobraziya s ekviaffinnymi svyaznostyami”, Matematika v obrazovanii: 200 let vysshemu matematicheskomu obrazovaniyu Rossii, Sb. statei pod red I. S. Emelyanovoi, Izd-vo Chuvash. un-ta, Cheboksary, 2005, 246–250

[14] Chentsov N. N., Statisticheskie reshayuschie pravila i optimalnye vyvody, Nauka, M., 1972

[15] Agricola I., “Nonintegrable geometries, torsion, and holonomy”, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, IRMA Lect. Math. Theor. Phys., 16, Eur. Math. Soc., Zürich, 2010, 277–346 | MR | Zbl

[16] Agricola I., Ferreira A. C., “Einshtein manifolds with skew-torsion”, Quart. J. Math., 65 (2014), 717–741 | DOI | MR | Zbl

[17] Amari S. I., “Differential-geometrical methods in statistics”, Lect. Notes Stat., v. 28, Springer-Verlag, Berlin, 1985 | DOI | MR | Zbl

[18] Draper C., Garvin A., Palomo F. J., “Invariant affine connections on odd-dimensional spheres”, Ann. Glob. Anal. Geom., 49 (2016), 213–251 | DOI | MR | Zbl

[19] Draper C., Palomo F. J., “Homogeneous Riemann–Cartan spheres”, Pure and Applied Differential Geometry: PADGE 2012. In memory of Franki Dillen (J. Van der Veken et al, eds.), Proc. Int. Conf. Leuven (Belgium, August 27–30, 2012), Shaker, Aachen, 2013, 126–135 | Zbl

[20] Gordeeva I. A., Panzhensky V. I., Stepanov S. E., “Riemann—Cartan manifolds”, J. Math. Sci., 169:3 (2009), 342–361 | DOI | MR

[21] Montgomery D., Samelson H., “Transformation groups of spheres”, Ann. Math. (2), 44 (1943), 454–470 | DOI | MR | Zbl

[22] Panzhenskii V. I., “Infinitesimal automorphisms of metric structures of Finsler type”, J. Math. Sci., 169:3 (2010), 297–313 | DOI | MR

[23] Panzhensky V. I., “Automorphisms of Riemann–Cartan manifolds with semi-symmetric connection”, J. Math. Phys. Anal. Geom., 10:2 (2014), 233–239 | MR | Zbl

[24] Panzhenskii V. I., Surina O. P., “Automorphisms of spacetime manifold with torsion”, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math., 55:1 (2016), 87–94 | MR | Zbl

[25] Rao C. R., “Information and accuracy attainable in the of statistical parameters”, Bull. Calcutta Math. Soc., 37 (1945), 81–89 | MR