Geodesic
Metric of special 2F-flat Riemannian spaces
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 7-11 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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: $F^3=I$.
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: $F^3=I$.
Classification : 53B20, 53B30, 53B35, 53C15
Keywords: $2F$-flat (pseudo-)Riemannian spaces; $2F$-planar mapping; cubic structure 
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Al Lamy, Raad J. Metric of special 2F-flat Riemannian spaces. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 7-11. http://geodesic.mathdoc.fr/item/AUPO_2005_44_1_a0/

[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

[2] Eisenhart L. P.: Riemannian Geometry. : Princenton Univ. Press. 1926. | MR

[3] Kurbatova I. N.: HP-mappings of H-spaces. Ukr. Geom. Sb., Kharkov, 27 (1984), 75–82. | MR | Zbl

[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

[7] J. Mikeš: On special F-planar mappings of affine-connected spaces. Vestn. Mosk. Univ., 1994, 3, 18–24. | MR

[8] Mikeš J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci., New York, 78, 3 (1996), 311–333. | MR | Zbl

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

[10] Mikeš J., Pokorná O.: On holomorphically projective mappings onto Kählerian spaces. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, (2002), 181–186. | MR | Zbl

[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 | Zbl

[12] Petrov A. Z.: New Method in General Relativity Theory. : Nauka, Moscow. 1966. | MR

[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

[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

[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 | Zbl

[18] Yano K.: Differential Geometry on Complex, Almost Complex Spaces. : Pergamon Press, Oxford–London–New York–Paris–Frankfurt. XII, 1965, 323p. | MR