| Title:
             | 
On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds (English) | 
| Author:
             | 
Hinterleitner, Irena | 
| Author:
             | 
Mikeš, Josef | 
| Language:
             | 
English | 
| Journal:
             | 
Archivum Mathematicum | 
| ISSN:
             | 
0044-8753 (print) | 
| ISSN:
             | 
1212-5059 (online) | 
| Volume:
             | 
49 | 
| Issue:
             | 
5 | 
| Year:
             | 
2013 | 
| Pages:
             | 
295-302 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics. (English) | 
| Keyword:
             | 
holomorphically projective mapping | 
| Keyword:
             | 
smoothness class | 
| Keyword:
             | 
Kähler manifold | 
| Keyword:
             | 
manifold with affine connection | 
| Keyword:
             | 
fundamental equation | 
| MSC:
             | 
32Q15 | 
| MSC:
             | 
53B20 | 
| MSC:
             | 
53B21 | 
| MSC:
             | 
53B30 | 
| MSC:
             | 
53B35 | 
| MSC:
             | 
53C26 | 
| idZBL:
             | 
Zbl 06383791 | 
| idMR:
             | 
MR3159328 | 
| DOI:
             | 
10.5817/AM2013-5-295 | 
| . | 
| Date available:
             | 
2014-01-16T11:18:57Z | 
| Last updated:
             | 
2015-03-19 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/143553 | 
| . | 
| Reference:
             | 
[1] al Lami, R. J. K., Škodová, M., Mikeš, J.: On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces.Arch. Math. (Brno) 42 (5) (2006), 291–299. Zbl 1164.53317, MR 2322415 | 
| Reference:
             | 
[2] Alekseevsky, D. V., Marchiafava, S.: Transformation of a quaternionic Kaehlerian manifold.C. R. Acad. Sci. Paris, Ser. I 320 (1995), 703–708. | 
| Reference:
             | 
[3] Apostolov, V., Calderbank, D. M. J., Gauduchon, P., Tønnesen–Friedman, Ch. W.: Extremal Kähler metrics on projective bundles over a curve.Adv. Math. 227 (6) (2011), 2385–2424. Zbl 1232.32011, MR 2807093, 10.1016/j.aim.2011.05.006 | 
| Reference:
             | 
[4] Beklemishev, D.V.: Differential geometry of spaces with almost complex structure.Geometria. Itogi Nauki i Tekhn., VINITI, Akad. Nauk SSSR, Moscow (1965), 165–212. | 
| Reference:
             | 
[5] Domashev, V. V., Mikeš, J.: Theory of holomorphically projective mappings of Kählerian spaces.Math. Notes 23 (1978), 160–163, transl. from Mat. Zametki 23(2) (1978), 297–304. 10.1007/BF01153160 | 
| Reference:
             | 
[6] Eisenhart, L. P.: Non–Riemannian Geometry.Princeton Univ. Press, 1926, AMS Colloq. Publ. 8 (2000). | 
| Reference:
             | 
[7] Hinterleitner, I.: On holomorphically projective mappings of e–Kähler manifolds.Arch. Math. (Brno) 48 (2012), 333–338. Zbl 1289.53038, MR 3007616, 10.5817/AM2012-5-333 | 
| Reference:
             | 
[8] Hinterleitner, I., Mikeš, J.: On F–planar mappings of spaces with affine connections.Note Mat. 27 (2007), 111–118. Zbl 1150.53009, MR 2367758 | 
| Reference:
             | 
[9] Hinterleitner, I., Mikeš, J.: Fundamental equations of geodesic mappings and their generalizations.J. Math. Sci. 174 (5) (2011), 537–554. Zbl 1283.53015, 10.1007/s10958-011-0316-8 | 
| Reference:
             | 
[10] Hinterleitner, I., Mikeš, J.: Projective equivalence and spaces with equi–affine connection.J. Math. Sci. 177 (2011), 546–550, transl. from Fundam. Prikl. Mat. 16 (2010), 47–54. MR 2786490, 10.1007/s10958-011-0479-3 | 
| Reference:
             | 
[11] Hinterleitner, I., Mikeš, J.: Geodesic Mappings and Einstein Spaces.Geometric Methods in Physics, Birkhäuser Basel, 2013, arXiv: 1201.2827v1 [math.DG], 2012, pp. 331–336. Zbl 1268.53049 | 
| Reference:
             | 
[12] Hinterleitner, I., Mikeš, J.: Geodesic mappings of (pseudo-) Riemannian manifolds preserve class of differentiability.Miskolc Math. Notes 14 (2) (2013), 575–582. Zbl 1299.53041, MR 3144094 | 
| Reference:
             | 
[13] Hrdina, J.: Almost complex projective structures and their morphisms.Arch. Math. (Brno) 45 (2009), 255–264. Zbl 1212.53022, MR 2591680 | 
| Reference:
             | 
[14] Hrdina, J., Slovák, J.: Morphisms of almost product projective geometries.Proc. 10th Int. Conf. on Diff. Geom. and its Appl., DGA 2007, Olomouc, Hackensack, NJ: World Sci., 2008, pp. 253–261. Zbl 1168.53013, MR 2462798 | 
| Reference:
             | 
[15] Jukl, M., Juklová, L., Mikeš, J.: Some results on traceless decomposition of tensors.J. Math. Sci. 174 (2011), 627–640. 10.1007/s10958-011-0321-y | 
| Reference:
             | 
[16] Mikeš, J.: On holomorphically projective mappings of Kählerian spaces.Ukrain. Geom. Sb. 23 (1980), 90–98. Zbl 0463.53013 | 
| Reference:
             | 
[17] Mikeš, J.: Special F—planar mappings of affinely connected spaces onto Riemannian spaces.Moscow Univ. Math. Bull. 49 (1994), 15–21, transl. from Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1994, 18–24. Zbl 0896.53035 | 
| Reference:
             | 
[18] Mikeš, J.: Holomorphically projective mappings and their generalizations.J. Math. Sci. 89 (1998), 13334–1353. 10.1007/BF02414875 | 
| Reference:
             | 
[19] Mikeš, J., Pokorná, O.: On holomorphically projective mappings onto Kählerian spaces.Rend. Circ. Mat. Palermo (2) Suppl. 69 (2002), 181–186. Zbl 1023.53015, MR 1972433 | 
| Reference:
             | 
[20] Mikeš, J., Shiha, M., Vanžurová, A.: Invariant objects by holomorphically projective mappings of Kähler spaces.8th Int. Conf. APLIMAT 2009, 2009, pp. 439–444. | 
| Reference:
             | 
[21] Mikeš, J., Sinyukov, N. S.: On quasiplanar mappings of space of affine connection.Sov. Math. 27 (1983), 63–70, transl. from Izv. Vyssh. Uchebn. Zaved. Mat.. | 
| Reference:
             | 
[22] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and some Generalizations.Palacky University Press, Olomouc, 2009. Zbl 1222.53002, MR 2682926 | 
| Reference:
             | 
[23] Otsuki, T., Tashiro, Y.: On curves in Kaehlerian spaces.Math. J. Okayama Univ. 4 (1954), 57–78. Zbl 0057.14101 | 
| Reference:
             | 
[24] Petrov, A . Z.: Simulation of physical fields.Gravitatsiya i Teor. Otnositelnosti 4–5 (1968), 7–21. | 
| Reference:
             | 
[25] Prvanović, M.: Holomorphically projective transformations in a locally product space.Math. Balkanica 1 (1971), 195–213. | 
| Reference:
             | 
[26] Sinyukov, N. S.: Geodesic mappings of Riemannian spaces.Moscow: Nauka, 1979. Zbl 0637.53020 | 
| Reference:
             | 
[27] Škodová, M., Mikeš, J., Pokorná, O.: On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces.Rend. Circ. Mat. Palermo (2) Suppl. 75 (2005), 309–316. Zbl 1109.53019, MR 2152369 | 
| Reference:
             | 
[28] Stanković, M. S., Zlatanović, M. L., Velimirović, L. S.: Equitorsion holomorphically projective mappings of generalized Kaehlerian space of the first kind.Czechoslovak Math. J. 60 (2010), 635–653. Zbl 1224.53031, MR 2672406, 10.1007/s10587-010-0059-6 | 
| Reference:
             | 
[29] Yano, K.: Differential geometry on complex and almost complex spaces.vol. XII, Pergamon Press, 1965. Zbl 0127.12405 | 
| . |