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Keywords:
holomorphically projective mappings; smoothness class; Kähler space; hyperbolic Kähler space
Summary:
In this paper we study fundamental equations of holomorphically projective mappings of $e$-Kähler spaces (i.e. classical, pseudo- and hyperbolic Kähler spaces) with respect to the smoothness class of metrics. We show that holomorphically projective mappings preserve the smoothness class of metrics.
References:
[1] Alekseevsky, D. V.: Pseudo–Kähler and para–Kähler symmetric spaces. Handbook of pseudo–Riemannian geometry and supersymmetry. ndbook of pseudo–Riemannian geometry and supersymmetry, IRMA Lect. Math. Theor. Phys. 16 (2010), 703–729. MR 2681606
[2] Beklemishev, D. V.: Differential geometry of spaces with almost complex structure. Akad. Nauk SSSR Inst. Naučn. Informacii, Moscow, 1965 Geometry (1963), 165–212. MR 0192434
[3] Domashev, V. V., Mikeš, J.: Theory of holomorphically projective mappings of Kählerian spaces. Math. Notes 23 (1978), 160–163. DOI 10.1007/BF01153160
[4] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces. Geometric Methods in Physics, XXX Workshop in Białowieża, Poland 2011, arXiv:1201.2827v1 [math.DG], 2012.
[5] Kähler, E.: Über eine bemerkenswerte Hermitesche Metrik. Sem. Hamburg. Univ. 9 (1933), 173–186. DOI 10.1007/BF02940642
[6] Kurbatova, I. N.: HP–mappings of H–spaces. Ukrain. Geom. Sb. 27 (1984), 75–83. MR 0767421 | Zbl 0571.58006
[7] Mikeš, J.: Geodesic and holomorphically projective mappings of special Riemannian spaces. Ph.D. thesis, Odessa, 1979.
[8] Mikeš, J.: On holomorphically projective mappings of Kählerian spaces. Ukrain. Geom. Sb. 23 (1980), 90–98. Zbl 0463.53013
[9] Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. 89 (1998), 1334–1353. DOI 10.1007/BF02414875 | MR 1619720
[10] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic mappings and some generalizations. Palacky University Press, Olomouc, 2009. MR 2682926 | Zbl 1222.53002
[11] Otsuki, T., Tashiro, Y.: On curves in Kaehlerian spaces. Math. J. Okayama Univ. 4 (1954), 57–78. MR 0066024 | Zbl 0057.14101
[12] Prvanović, M.: Holomorphically projective transformations in a locally product space. Math. Balkanica 1 (1971), 195–213. MR 0288710
[13] Rashevsky, P. A.: Scalar fields in fibered space. Trudy Sem. Vektor. Tenzor. Anal. 6 (1948), 225–248.
[14] Shirokov, P. A.: Selected investigations on geometry. Kazan' University Press, 1966.
[15] Sinyukov, N. S.: Geodesic mappings of Riemannian spaces. Moscow, Nauka, 1979. MR 0552022 | Zbl 0637.53020
[16] Sinyukov, N. S., Kurbatova, I. N., Mikeš, J.: Holomorphically projective mappings of Kähler spaces. Odessa, Odessk. Univ., 1985.
[17] 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 2152369 | Zbl 1109.53019
[18] Tachibana, S.–I., Ishihara, S.: On infinitesimal holomorphically projective transformations in Kählerian manifolds. Tôhoku Math. J. (2) 12 (1960), 77–101. DOI 10.2748/tmj/1178244489 | MR 0120599 | Zbl 0093.35404
[19] Yano, K.: Differential geometry of complex and almost comlex spaces. Pergamon Press, 1965.
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