Keywords: holomorphically projective mapping; smoothness class; Kähler manifold; manifold with affine connection; fundamental equation
@article{10_5817_AM2013_5_295,
author = {Hinterleitner, Irena and Mike\v{s}, Josef},
title = {On holomorphically projective mappings from manifolds with equiaffine connection onto {K\"ahler} manifolds},
journal = {Archivum mathematicum},
pages = {295--302},
year = {2013},
volume = {49},
number = {5},
doi = {10.5817/AM2013-5-295},
mrnumber = {3159328},
zbl = {06383791},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-295/}
}
TY - JOUR AU - Hinterleitner, Irena AU - Mikeš, Josef TI - On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds JO - Archivum mathematicum PY - 2013 SP - 295 EP - 302 VL - 49 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-295/ DO - 10.5817/AM2013-5-295 LA - en ID - 10_5817_AM2013_5_295 ER -
%0 Journal Article %A Hinterleitner, Irena %A Mikeš, Josef %T On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds %J Archivum mathematicum %D 2013 %P 295-302 %V 49 %N 5 %U http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-295/ %R 10.5817/AM2013-5-295 %G en %F 10_5817_AM2013_5_295
Hinterleitner, Irena; Mikeš, Josef. On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds. Archivum mathematicum, Tome 49 (2013) no. 5, pp. 295-302. doi: 10.5817/AM2013-5-295
[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. | MR | Zbl
[2] Alekseevsky, D. V., Marchiafava, S.: Transformation of a quaternionic Kaehlerian manifold. C. R. Acad. Sci. Paris, Ser. I 320 (1995), 703–708.
[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. | DOI | MR | Zbl
[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.
[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. | DOI
[6] Eisenhart, L. P.: Non–Riemannian Geometry. Princeton Univ. Press, 1926, AMS Colloq. Publ. 8 (2000).
[7] Hinterleitner, I.: On holomorphically projective mappings of e–Kähler manifolds. Arch. Math. (Brno) 48 (2012), 333–338. | DOI | MR | Zbl
[8] Hinterleitner, I., Mikeš, J.: On F–planar mappings of spaces with affine connections. Note Mat. 27 (2007), 111–118. | MR | Zbl
[9] Hinterleitner, I., Mikeš, J.: Fundamental equations of geodesic mappings and their generalizations. J. Math. Sci. 174 (5) (2011), 537–554. | DOI | Zbl
[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. | DOI | MR
[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
[12] Hinterleitner, I., Mikeš, J.: Geodesic mappings of (pseudo-) Riemannian manifolds preserve class of differentiability. Miskolc Math. Notes 14 (2) (2013), 575–582. | MR | Zbl
[13] Hrdina, J.: Almost complex projective structures and their morphisms. Arch. Math. (Brno) 45 (2009), 255–264. | MR | Zbl
[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. | MR | Zbl
[15] Jukl, M., Juklová, L., Mikeš, J.: Some results on traceless decomposition of tensors. J. Math. Sci. 174 (2011), 627–640. | DOI
[16] Mikeš, J.: On holomorphically projective mappings of Kählerian spaces. Ukrain. Geom. Sb. 23 (1980), 90–98. | Zbl
[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
[18] Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. 89 (1998), 13334–1353. | DOI
[19] Mikeš, J., Pokorná, O.: On holomorphically projective mappings onto Kählerian spaces. Rend. Circ. Mat. Palermo (2) Suppl. 69 (2002), 181–186. | MR | Zbl
[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.
[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..
[22] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and some Generalizations. Palacky University Press, Olomouc, 2009. | MR | Zbl
[23] Otsuki, T., Tashiro, Y.: On curves in Kaehlerian spaces. Math. J. Okayama Univ. 4 (1954), 57–78. | Zbl
[24] Petrov, A . Z.: Simulation of physical fields. Gravitatsiya i Teor. Otnositelnosti 4–5 (1968), 7–21.
[25] Prvanović, M.: Holomorphically projective transformations in a locally product space. Math. Balkanica 1 (1971), 195–213.
[26] Sinyukov, N. S.: Geodesic mappings of Riemannian spaces. Moscow: Nauka, 1979. | Zbl
[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. | MR | Zbl
[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. | DOI | MR | Zbl
[29] Yano, K.: Differential geometry on complex and almost complex spaces. vol. XII, Pergamon Press, 1965. | Zbl
Cité par Sources :