On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces
Raad J. K. al Lami; Marie Škodová; Josef Mikeš
Archivum Mathematicum (2006)
- Volume: 042, Issue: 5, page 291-299
- ISSN: 0044-8753
Access Full Article
topAbstract
topHow to cite
topal Lami, Raad J. K., Škodová, Marie, and Mikeš, Josef. "On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces." Archivum Mathematicum 042.5 (2006): 291-299. <http://eudml.org/doc/249827>.
@article{alLami2006,
abstract = {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.},
author = {al Lami, Raad J. K., Škodová, Marie, Mikeš, Josef},
journal = {Archivum Mathematicum},
keywords = {Kählerian space; Ricci tensor; curvature operator; holomorphically projective mapping},
language = {eng},
number = {5},
pages = {291-299},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces},
url = {http://eudml.org/doc/249827},
volume = {042},
year = {2006},
}
TY - JOUR
AU - al Lami, Raad J. K.
AU - Škodová, Marie
AU - Mikeš, Josef
TI - On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 291
EP - 299
AB - 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.
LA - eng
KW - Kählerian space; Ricci tensor; curvature operator; holomorphically projective mapping
UR - http://eudml.org/doc/249827
ER -
References
top- Boeckx E., Kowalski O., Vanhecke L., Riemannian manifolds of conullity two, World Sci. 1996. (1996) Zbl0904.53006MR1462887
- 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) Zbl0406.53052MR0492674
- Eisenhart L. P., Non-Riemannian Geometry, Princenton Univ. Press. 1927, Colloquium Publ. Vol. 8., AMS, Providence, 2003. (1927) MR0035081
- 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) Zbl0444.53032MR0581924
- Kaygorodov V. R., On Riemannian spaces , 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) MR0697392
- Lakomá L., Jukl M., The decomposition of tensor spaces with almost complex structure, Rend. Circ. Mat. Palermo (2) Suppl. 72 (2004), 145–150. Zbl1064.53015MR2069402
- Mikeš J., On holomorphically projective mappings of Kählerian spaces, Ukr. Geom. Sb., Kharkov, 23 (1980), 90–98. (1980) Zbl0463.53013
- Mikeš J., On geodesic mappings of -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) Zbl0816.53009MR1233688
- 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) Zbl0835.53049MR1302090
- Mikeš J., On special F-planar mappings of affine-connected spaces, Vestn. Moskov. Univ. 3 (1994), 18–24. (1994) MR1315721
- 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) MR1406322
- Mikeš J., Geodesic mappings of affine-connected and Riemannian spaces, J. Math. Sci. (New York) 78 3 (1996), 311–333. (1996) Zbl0866.53028MR1384327
- Mikeš J., Holomorphically projective mappings and their generalizations, J. Math. Sci. (New York) 89 3 (1998), 1334–1353. (1998) Zbl0983.53013MR1619720
- Mikeš J., Pokorná O., On holomorphically projective mappings onto Kählerian spaces, Rend. Circ. Mat. Palermo (2) Suppl. 69 (2002), 181–186. Zbl1023.53015MR1972433
- Mikeš J., Radulović Ž., Haddad M., Geodesic and holomorphically projective mappings of -pseudo- and -quasisymmetric Riemannian spaces, Russ. Math. 40 10 (1996), 28–32; Izv. Vyssh. Uchebn. Mat. 10 (413) (1996), 30–35. (1996) Zbl0890.53041MR1447076
- Mikeš J., Rachůnek L., -semisymmetric spaces and concircular vector fields, Rend. Circ. Mat. Palermo (2) Suppl. 69 (2002), 187–193. (193.) MR1972434
- 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) Zbl0526.53013MR0694014
- Otsuki T., Tashiro Y., On curves in Kaehlerian spaces, Math. J. Okayama Univ. 4 (1954), 57–78. (1954) Zbl0057.14101MR0066024
- 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) Zbl0305.53024MR0370411
- 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) Zbl0637.53020MR0552022
- 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. Zbl1109.53019MR2152369
- Sobchuk V. S., Mikeš J., Pokorná O., On almost geodesic mappings between semisymmetric Riemannian spaces, Novi Sad J. Math. 29 3 (1999), 309–312. (1999) Zbl1012.53015MR1771008
- 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) Zbl0127.12405MR0187181
Citations in EuDML Documents
top- Raad J. K. al Lami, Holomorphically projective mappings of compact semisymmetric manifolds
- Irena Hinterleitner, Josef Mikeš, On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds
- Irena Hinterleitner, Josef Mikeš, Patrik Peška, On -planar mappings of (pseudo-) Riemannian manifolds
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.