Previous |  Up |  Next

Article

Keywords:
$2F$-flat (pseudo-)Riemannian spaces; $2F$-planar mapping; cubic structure
Summary:
In this paper we find the metric in an explicit shape of special $2F$-flat Riemannian spaces $V_n$, i.e. spaces, which are $2F$-planar mapped on flat spaces. In this case it is supposed, that $F$ is the cubic structure: $F^3=I$.
References:
[1] Beklemishev D. V.: Differential geometry of spaces with almost complex structure. Geometria. Itogi Nauki i Tekhn., All-Union Inst. for Sci. and Techn. Information (VINITI), Akad. Nauk SSSR, Moscow, 1965, 165–212. MR 0192434
[2] Eisenhart L. P.: Riemannian Geometry. : Princenton Univ. Press. 1926. MR 1487892
[3] Kurbatova I. N.: HP-mappings of H-spaces. Ukr. Geom. Sb., Kharkov, 27 (1984), 75–82. MR 0767421 | Zbl 0571.58006
[4] Al Lamy R. J.: About 2F-plane mappings of affine connection spaces. Coll. on Diff. Geom., Eger (Hungary), 1989, 20–25.
[5] Al Lamy R. J., Kurbatova I. N.: Invariant geometric objects of 2F-planar mappings of affine connection spaces and Riemannian spaces with affine structure of III order. Dep. of UkrNIINTI (Kiev), 1990, No. 1004Uk90, 51p.
[6] Al Lamy R. J., Mikeš J., Škodová M.: On linearly $pF$-planar mappings. Diff. Geom. and its Appl. Proc. Conf. Prague, 2004, Charles Univ., Prague (Czech Rep.), 2005, 347–353. Zbl 1114.53012
[7] J. Mikeš: On special F-planar mappings of affine-connected spaces. Vestn. Mosk. Univ., 1994, 3, 18–24. MR 1315721
[8] Mikeš J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci., New York, 78, 3 (1996), 311–333. MR 1384327 | Zbl 0866.53028
[9] Mikeš J.: Holomorphically projective mappings and their generalizations. J. Math. Sci., New York, 89, 3 (1998), 1334–1353. MR 1619720 | Zbl 0983.53013
[10] Mikeš J., Pokorná O.: On holomorphically projective mappings onto Kählerian spaces. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, (2002), 181–186. MR 1972433 | Zbl 1023.53015
[11] Mikeš J., Sinyukov N. S.: On quasiplanar mappings of spaces of affine connection. Sov. Math. 27, 1 (1983), 63–70; translation from Izv. Vyssh. Uchebn. Zaved., Mat., 248, 1 (1983), 55–61. MR 0694014 | Zbl 0526.53013
[12] Petrov A. Z.: New Method in General Relativity Theory. : Nauka, Moscow. 1966. MR 0207365
[13] Petrov A. Z.: Simulation of physical fields. In: Gravitation and the Theory of Relativity, Vol. 4–5, Kazan’ State Univ., Kazan, 1968, 7–21. MR 0285249
[14] Shirokov P. A.: Selected Work in Geometry. : Kazan State Univ. Press, Kazan. 1966.
[15] Sinyukov N. S.: Geodesic Mappings of Riemannian Spaces. : Nauka, Moscow. 1979. MR 0552022
[16] Sinyukov N. S.: Almost geodesic mappings of affinely connected and Riemannian spaces. J. Sov. Math. 25 (1984), 1235–1249.
[17] Škodová M., Mikeš J., Pokorná O.: On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces. Circ. Mat. di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 75, (2005), 309–316. MR 2152369 | Zbl 1109.53019
[18] Yano K.: Differential Geometry on Complex, Almost Complex Spaces. : Pergamon Press, Oxford–London–New York–Paris–Frankfurt. XII, 1965, 323p. MR 0187181
Partner of
EuDML logo