Previous |  Up |  Next

Article

Keywords:
non-symmetric affine connection; almost geodesic mapping; $G$-almost geodesic mapping; property of reciprocity; almost geodesic mapping of the second type
Summary:
We study $G$-almost geodesic mappings of the second type $\underset \theta \to \pi _2(e)$, $\theta =1,2$ between non-symmetric affine connection spaces. These mappings are a generalization of the second type almost geodesic mappings defined by N. S. Sinyukov (1979). We investigate a special type of these mappings in this paper. We also consider $e$-structures that generate mappings of type $\underset \theta \to \pi _2(e)$, $\theta =1,2$. For a mapping $\underset \theta \to \pi _2(e,F)$, $\theta =1,2$, we determine the basic equations which generate them.
References:
[1] Berezovskij, V., Mikeš, J.: On a classification of almost geodesic mappings of affine connection spaces. Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 35 (1996), 21-24. MR 1485039
[2] Berezovski, V. E., Mikeš, J., Vanžurová, A.: Fundamental PDE's of the canonical almost geodesic mappings of type ${\tilde\pi_1}$. Bull. Malays. Math. Sci. Soc. (2) 37 (2014), 647-659. MR 3234506 | Zbl 1298.53018
[3] Hall, G. S., Lonie, D. P.: Projective equivalence of Einstein spaces in general relativity. Classical Quantum Gravity 26 (2009), Article ID 125009, 10 pages. DOI 10.1088/0264-9381/26/12/125009 | MR 2515670 | Zbl 1170.83443
[4] Hall, G. S., Lonie, D. P.: The principle of equivalence and cosmological metrics. J. Math. Phys. 49 Article ID 022502, 13 pages (2008). MR 2392851 | Zbl 1153.81370
[5] Hall, G. S., Lonie, D. P.: The principle of equivalence and projective structure in spacetimes. Classical Quantum Gravity 24 (2007), 3617-3636. DOI 10.1088/0264-9381/24/14/005 | MR 2339411 | Zbl 1206.83036
[6] Hinterleitner, I.: Geodesic mappings on compact Riemannian manifolds with conditions on sectional curvature. Publ. Inst. Math. (Beograd) (N.S.) 94 (2013), 125-130, DOI:10.2298/PIM1308125H. DOI 10.2298/PIM1308125H | MR 3137496
[7] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces. Geometric Methods in Physics P. Kielanowski, et al. Selected papers of 30. workshop, Białowie$\dot z$a, 2011. Trends in Mathematics Birkhäuser, Basel (2013), 331-335. MR 2882715 | Zbl 1268.53049
[8] Hinterleitner, I., Mikeš, J.: Geodesic mappings of (pseudo-) Riemannian manifolds preserve class of differentiability. Miskolc Math. Notes 14 (2013), 575-582. MR 3144094
[9] Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci., New York 89 (1998), 1334-1353 translation from Itogi Nauki Tekh., Ser. Sovrem Mat. Prilozh., Temat. Obz. 30 258-291 (1995). DOI 10.1007/BF02414875 | MR 1619720
[10] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci., New York 78 (1996), 311-333. DOI 10.1007/BF02365193 | MR 1384327
[11] Mikeš, J.: Geodesic mappings of Einstein spaces. Math. Notes 28 (1981), 922-923 translation from Mat. Zametki 28 935-938, DOI:10.1007/BF01709156 Russian (1980). DOI 10.1007/BF01709156 | MR 0603226 | Zbl 0454.53018
[12] Mikeš, J., Pokorná, O., Starko, G.: On almost geodesic mappings ${\pi_2(e)}$ onto Riemannian spaces. J. Slovák, et al. The Proceedings of the 23th Winter School Geometry and Physics, Srní, 2003 Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 72 (2004), 151-157. MR 2069403 | Zbl 1050.53021
[13] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations. Palacký University, Faculty of Science, Olomouc (2009). MR 2682926 | Zbl 1222.53002
[14] Minčić, S. M.: New commutation formulas in the non-symmetric affine connexion space. Publ. Inst. Math., Nouv. Sér. 22 (1977), 189-199. MR 0482552 | Zbl 0377.53008
[15] Minčić, S. M.: Ricci identities in the space of non-symmetric affine connexion. Mat. Vesn., N. Ser. 10 (1973), 161-172. MR 0341310 | Zbl 0278.53012
[16] Minčić, S. M., Stanković, M. S.: Equitorsion geodesic mappings of generalized Riemannian spaces. Publ. Inst. Math., Nouv. Sér. 61 (1997), 97-104. MR 1472941 | Zbl 0886.53035
[17] Minčić, S., Stanković, M.: On geodesic mappings of general affine connexion spaces and of generalized Riemannian spaces. Mat. Vesn. 49 (1997), 27-33. MR 1491944 | Zbl 0949.53013
[18] Sinyukov, N. S.: Geodesic Mappings of Riemannian Spaces. Russian Nauka, Moskva (1979). MR 0552022 | Zbl 0637.53020
[19] Stanković, M.: On a special almost geodesic mapping of third type of affine spaces. Novi Sad J. Math. 31 (2001), 125-135. MR 1897496 | Zbl 1012.53013
[20] Stanković, M. S.: First type almost geodesic mappings of general affine connection spaces. Novi Sad J. Math. 29 (1999), 313-323. MR 1771009 | Zbl 0951.53011
[21] Stanković, M. S.: On canonic almost geodesic mappings of the second type of affine spaces. Filomat 13 (1999), 105-114. MR 1803017 | Zbl 0971.53011
[22] Stanković, M. S., Minčić, S. M.: New special geodesic mappings of generalized Riemannian spaces. Publ. Inst. Math., Nouv. Sér. 67 (2000), 92-102. MR 1761305 | Zbl 1013.53009
[23] Vavříková, H., Mikeš, J., Pokorná, O., Starko, G.: On fundamental equations of almost geodesic mappings of type ${\pi_2(e)}$. Russ. Math. 51 8-12 (2007), translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2007 10-15 (2007), Russian. DOI 10.3103/S1066369X07010021 | MR 2335593 | Zbl 1143.53019
Partner of
EuDML logo