On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces
al Lami, Raad J. K. ; Škodová, Marie ; Mikeš, Josef
Archivum Mathematicum, Tome 042 (2006), p. 291-299 / Harvested from Czech Digital Mathematics Library

In this paper we consider holomorphically projective mappings from the special generally recurrent equiaffine spaces $A_n$ onto (pseudo-) Kählerian spaces $\bar{K}_n$. We proved that these spaces $A_n$ do not admit nontrivial holomorphically projective mappings onto $\bar{K}_n$. These results are a generalization of results by T. Sakaguchi, J. Mikeš and V. V. Domashev, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.

Publié le : 2006-01-01
Classification:  53B20,  53B30,  53B35
@article{108035,
     author = {Raad J. K. al Lami and Marie \v Skodov\'a and Josef Mike\v s},
     title = {On holomorphically projective mappings from equiaffine generally recurrent spaces onto K\"ahlerian spaces},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {291-299},
     zbl = {1164.53317},
     mrnumber = {2322415},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108035}
}
al Lami, Raad J. K.; Škodová, Marie; Mikeš, Josef. On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces. Archivum Mathematicum, Tome 042 (2006) pp. 291-299. http://gdmltest.u-ga.fr/item/108035/

Boeckx E.; Kowalski O.; Vanhecke L. Riemannian manifolds of conullity two, World Sci. 1996. (1996) | MR 1462887 | Zbl 0904.53006

Domashev V. V.; Mikeš J. Theory of holomorphically projective mappings of Kählerian spaces, Math. Notes 23 (1978), 160–163; translation from Mat. Zametki, 23 2 (1978), 297–304. (1978) | MR 0492674 | Zbl 0406.53052

Eisenhart L. P. Non-Riemannian Geometry, Princenton Univ. Press. 1927, Colloquium Publ. Vol. 8., AMS, Providence, 2003. (1927) | MR 0035081

Gray A.; Hervella L. M. The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. (4) 123 (1980), 35–58. (1980) | MR 0581924 | Zbl 0444.53032

Kaygorodov V. R. On Riemannian spaces $D_n^m$, Itogi Nauki i Tekhniki,Tr. Geom. Sem. Vol. 5, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow, 1974, 359–373. (1974)

Kaygorodov V. R. Structure of curvature of space-time, Itogi Nauki i Tekhniki, Problemy Geometrii, Vol. 14, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow, 1983, 177–204. (1983) | MR 0697392

Lakomá L.; Jukl M. The decomposition of tensor spaces with almost complex structure, Rend. Circ. Mat. Palermo (2) Suppl. 72 (2004), 145–150. | MR 2069402 | Zbl 1064.53015

Mikeš J. On holomorphically projective mappings of Kählerian spaces, Ukr. Geom. Sb., Kharkov, 23 (1980), 90–98. (1980) | Zbl 0463.53013

Mikeš J. On geodesic mappings of $m$-symmetric and generally semi-symmetric spaces, Russ. Math. 36 8 (1992), 38–42; translation from Izv. Vyssh. Uchebn. Zaved. Mat. 8 (363) (1992), 42–46. (1992) | MR 1233688 | Zbl 0816.53009

Mikeš J. Geodesic mappings onto semisymmetric spaces, Russ. Math. 38 2 (1994), 35–41; translation from Izv. Vyssh. Uchebn. Zaved. Mat. 2 (381) (1994), 37–43. (1994) | MR 1302090 | Zbl 0835.53049

Mikeš J. On special F-planar mappings of affine-connected spaces, Vestn. Moskov. Univ. 3 (1994), 18–24. (1994) | MR 1315721

Mikeš J. On the general trace decomposition problem, Differential Geom. Appl. Proc. Conf. Aug. 28 – Sept. 1, Brno, 1995, Czech Republic, Masaryk Univ., Brno 1996, 45–50. (1995) | MR 1406322

Mikeš J. Geodesic mappings of affine-connected and Riemannian spaces, J. Math. Sci. (New York) 78 3 (1996), 311–333. (1996) | MR 1384327 | Zbl 0866.53028

Mikeš J. Holomorphically projective mappings and their generalizations, J. Math. Sci. (New York) 89 3 (1998), 1334–1353. (1998) | MR 1619720 | Zbl 0983.53013

Mikeš J.; Pokorná O. On holomorphically projective mappings onto Kählerian spaces, Rend. Circ. Mat. Palermo (2) Suppl. 69 (2002), 181–186. | MR 1972433 | Zbl 1023.53015

Mikeš J.; Radulović Ž.; Haddad M. Geodesic and holomorphically projective mappings of $m$-pseudo- and $m$-quasisymmetric Riemannian spaces, Russ. Math. 40 10 (1996), 28–32; Izv. Vyssh. Uchebn. Mat. 10 (413) (1996), 30–35. (1996) | MR 1447076 | Zbl 0890.53041

Mikeš J.; Rachůnek L. $T$-semisymmetric spaces and concircular vector fields, Rend. Circ. Mat. Palermo (2) Suppl. 69 (2002), 187–193. (193.) | MR 1972434

Mikeš J.; Sinyukov N. S. On quasiplanar mappings of spaces of affine connection, (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1(248) (1983), 55–61; (English) Sov. Math. 27 1 (1983), 63–70. (1983) | MR 0694014 | Zbl 0526.53013

Otsuki T.; Tashiro Y. On curves in Kaehlerian spaces, Math. J. Okayama Univ. 4 (1954), 57–78. (1954) | MR 0066024 | Zbl 0057.14101

Petrov A. Z. New method in general relativity theory, Moscow, Nauka, 1966, 495p. (1966)

Sakaguchi T. On the holomorphically projective correspondence between Kählerian spaces preserving complex structure, Hokkaido Math. J. 3 (1974), 203–212. (1974) | MR 0370411 | Zbl 0305.53024

Shirokov P. A. Selected Work in Geometry, Kazan State Univ. Press, Kazan, 1966. (1966)

Sinyukov N. S. Geodesic mappings of Riemannian spaces, Moscow, Nauka, 1979, 256p. (1979) | MR 0552022 | Zbl 0637.53020

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

Sobchuk V. S.; Mikeš J.; Pokorná O. On almost geodesic mappings $\pi _2$ between semisymmetric Riemannian spaces, Novi Sad J. Math. 29 3 (1999), 309–312. (1999) | MR 1771008 | Zbl 1012.53015

Yano K. Concircular geometry. I-IV, Proc. Imp. Acad. Tokyo 16 (1940), 195–200, 354–360, 442–448, 505–511. (1940)

Yano K. Differential geometry on complex and almost complex spaces, Oxford-London-New York-Paris-Frankfurt, Pergamon Press 1965, XII, 323p. (1965) | MR 0187181 | Zbl 0127.12405