Conformal mappings onto Einstein spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 8-13.

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In the present paper we study conformal mappings of Riemannian manifolds onto an Einstein manifold for the minimal condition on the differentiability class of these manifolds. We show for which conditions the corresponding equations obtained by J. Mikeš, M. L. Gavril'chenko and E. I. Gladyscheva, which defined these mappings, are linear. We obtain the number of necessary parameters on which depends the general solution of fundamental system of equations.
Keywords: (pseudo-)Riemannian space, conformal mapping, Einstein space.
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L. E. Evtushik; I. Hinterleitner; N. I. Guseva; J. Mikeš. Conformal mappings onto Einstein spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 8-13. http://geodesic.mathdoc.fr/item/IVM_2016_10_a1/

[1] Eizenkhart L. P., Rimanova geometriya, In. lit., M., 1948

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

[3] Skhouten I. A., Stroik D. Dzh., Vvedenie v novye metody differentsialnoi geometrii, v. I, Gostekhizdat, M.–L., 1939

[4] Skhouten I. A., Stroik D. Dzh., Vvedenie v novye metody differentsiyaalnoi geometrii, v. II, Gostekhizdat, In. lit., M., 1949

[5] Denisov V. I., “Spetsialnye konformnye otobrazheniya v obschei teorii otnositelnosti”, Ukr. geometrich. sb., 28 (1985), 43–50 | MR | Zbl

[6] Brinkmann H. W., “Einstein spaces which mapped conformally on each other”, Math. Ann., 94 (1925), 117–145 | DOI | MR

[7] Mikesh I., Gavrilchenko M. L., Gladysheva E. I., “O konformnykh otobrazheniyakh na prostranstva Einshteina”, Vestn. Mosk. un-ta, 1994, no. 3, 13–17 | MR | Zbl

[8] Mikesh I., Gavrilchenko M. L., Gladysheva E. I., “O konformnykh otobrazheniyakh na prostranstva Einshteina”, Mezhdunarodn. nauchn. konf. “Lobachevskii i sovremennaya geometriya”, Tez. dokl. Ch. I (Kazan, 18–22 avgusta 1992 g.), Kazansk. un-t, 1992, 64

[9] Mikeš J., “Holomorphically projective mappings and their generalizations”, J. Math. Sci. (New York), 89:3 (1998), 1334–1353 | DOI | MR | Zbl

[10] Mikeš J., Vanžurová A., Hinterleitner I., Geodesic mappings and some generalizations, Palacky University Press, Olomouc, 2009 | MR | Zbl

[11] Evtushik L. E., Kiosak V. A., Mikesh I., “O mobilnosti rimanovykh prostranstv otnositelno konformnykh otobrazhenii na prostranstva Einshteina”, Izv. vuzov. Matem., 2010, no. 8, 36–41 | MR | Zbl

[12] Gover A. R., Nurowski P., “Obstructions to conformally Einstein metrics in $n$ dimensions”, J. Geom. Phys., 56:3 (2006), 450–484 | DOI | MR | Zbl

[13] Hammerl M., Somberg P., Souček V., Šilhan J., “Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry”, Ann. Global Anal. Geom., 42:1 (2012), 121–145 | DOI | MR | Zbl

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

[15] Yano K., Bochner S., Curvature and Betti numbers, Princeton Univ. Press, 1953 | MR | Zbl

[16] Hinterleitner I., Mikeš J., “Geodesic mappings and Einstein spaces”, Geom. Methods in Phys., Birkhauser, Basel, 2013, 331–335 ; 2012, arXiv: 1201.2827v1[math.DG] | DOI | MR | Zbl

[17] Hinterleitner I., Mikeš J., “On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds”, Arch. Math. (Brno), 49:5 (2013), 295–302 | DOI | MR | Zbl