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Title: Metric of special 2F-flat Riemannian spaces (English)
Author: Al Lamy, Raad J.
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 44
Issue: 1
Year: 2005
Pages: 7-11
Summary lang: English
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Category: math
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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: $F^3=I$. (English)
Keyword: $2F$-flat (pseudo-)Riemannian spaces
Keyword: $2F$-planar mapping
Keyword: cubic structure
MSC: 53B20
MSC: 53B30
MSC: 53B35
MSC: 53C15
idZBL: Zbl 1089.53020
idMR: MR2218562
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Date available: 2009-08-21T06:48:10Z
Last updated: 2012-05-04
Stable URL: http://hdl.handle.net/10338.dmlcz/133378
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Reference: [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
Reference: [2] Eisenhart L. P.: Riemannian Geometry. : Princenton Univ. Press., 1926. MR 1487892
Reference: [3] Kurbatova I. N.: HP-mappings of H-spaces.Ukr. Geom. Sb., Kharkov, 27 (1984), 75–82. Zbl 0571.58006, MR 0767421
Reference: [4] Al Lamy R. J.: About 2F-plane mappings of affine connection spaces.Coll. on Diff. Geom., Eger (Hungary), 1989, 20–25.
Reference: [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.
Reference: [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
Reference: [7] J. Mikeš: On special F-planar mappings of affine-connected spaces.Vestn. Mosk. Univ., 1994, 3, 18–24. MR 1315721
Reference: [8] Mikeš J.: Geodesic mappings of affine-connected and Riemannian spaces.J. Math. Sci., New York, 78, 3 (1996), 311–333. Zbl 0866.53028, MR 1384327
Reference: [9] Mikeš J.: Holomorphically projective mappings and their generalizations.J. Math. Sci., New York, 89, 3 (1998), 1334–1353. Zbl 0983.53013, MR 1619720
Reference: [10] Mikeš J., Pokorná O.: On holomorphically projective mappings onto Kählerian spaces.Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, (2002), 181–186. Zbl 1023.53015, MR 1972433
Reference: [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. Zbl 0526.53013, MR 0694014
Reference: [12] Petrov A. Z.: New Method in General Relativity Theory. : Nauka, Moscow., 1966. MR 0207365
Reference: [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
Reference: [14] Shirokov P. A.: Selected Work in Geometry. : Kazan State Univ. Press, Kazan., 1966.
Reference: [15] Sinyukov N. S.: Geodesic Mappings of Riemannian Spaces. : Nauka, Moscow., 1979. MR 0552022
Reference: [16] Sinyukov N. S.: Almost geodesic mappings of affinely connected and Riemannian spaces.J. Sov. Math. 25 (1984), 1235–1249.
Reference: [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. Zbl 1109.53019, MR 2152369
Reference: [18] Yano K.: Differential Geometry on Complex, Almost Complex Spaces. : Pergamon Press, Oxford–London–New York–Paris–Frankfurt., XII, 1965, 323p. MR 0187181
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