Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 635-653 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we define generalized Kählerian spaces of the first kind $(G\underset 1K_N)$ given by (2.1)--(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ($G\underset 1K_N$ and $G\underset 1{\overline K}_N$) and for them we find invariant geometric objects.
In this paper we define generalized Kählerian spaces of the first kind $(G\underset 1K_N)$ given by (2.1)--(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ($G\underset 1K_N$ and $G\underset 1{\overline K}_N$) and for them we find invariant geometric objects.
Classification : 53B05, 53B35
Keywords: generalized Riemannian space; Kählerian space; generalized Kählerian space of the first kind; equitorsion holomorphically projective mappings; holomorphically projective parameter.
@article{CMJ_2010_60_3_a3,
     author = {Stankovi\'c, Mi\'ca S. and Zlatanovi\'c, Milan Lj. and Velimirovi\'c, Ljubica S.},
     title = {Equitorsion holomorphically projective mappings of generalized {K\"ahlerian} space of the first kind},
     journal = {Czechoslovak Mathematical Journal},
     pages = {635--653},
     year = {2010},
     volume = {60},
     number = {3},
     mrnumber = {2672406},
     zbl = {1224.53031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a3/}
}
TY  - JOUR
AU  - Stanković, Mića S.
AU  - Zlatanović, Milan Lj.
AU  - Velimirović, Ljubica S.
TI  - Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 635
EP  - 653
VL  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a3/
LA  - en
ID  - CMJ_2010_60_3_a3
ER  - 
%0 Journal Article
%A Stanković, Mića S.
%A Zlatanović, Milan Lj.
%A Velimirović, Ljubica S.
%T Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind
%J Czechoslovak Mathematical Journal
%D 2010
%P 635-653
%V 60
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a3/
%G en
%F CMJ_2010_60_3_a3
Stanković, Mića S.; Zlatanović, Milan Lj.; Velimirović, Ljubica S. Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 635-653. http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a3/

[1] Chodorová, M., Mikeš, J.: A note to K-torse forming vector fields on compact manifolds with complex structure. Acta Physica Debrecina 42 (2008), 11-18. | MR

[2] Einstein, A.: The Bianchi identities in the generalized theory of gravitation. Can. J. Math. 2 (1950), 120-128. | DOI | MR | Zbl

[3] Einstein, A.: Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. 49 (1916), 769-822. | DOI

[4] Einstein, A.: Relativistic theory of the non-symmetic field. In: The Meaning of Relativity, 5th ed., Appendix II, Vol. 49 Princeton University Press Princeton (1955).

[5] Einstein, A.: Generalization of the relativistic theory of gravitation. Ann. Math. 46 (1945), 578-584. | DOI | MR | Zbl

[6] Eisenhart, L. P.: Generalized Riemannian spaces. Proc. Natl. Acad. Sci. 37 (1951), 311-315. | DOI | MR

[7] Hinterleitner, I., Mikeš, J.: On $F$-planar mappings of spaces with affine connections. Note Mat. 27 (2007), 111-118. | MR

[8] Hinterleitner, I., Mikeš, J., Stránská, J.: Infinitesimal $F$-planar transformations. Russ. Math. 52 (2008), 13-18. | DOI | MR

[9] Jukl, M., Juklová, L., Mikeš, J.: On Generalized Trace Decompositions Problems. Proc. 3rd International Conference dedicated to 85th birthday of Professor Kudrijavcev. (2008), 299-314.

[10] Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. 89 (1998), 1334-1353. | DOI | MR

[11] Mikeš, J., Starko, G. A.: $K$-concircular vector fields and holomorphically projective mappings on Kählerian spaces. Suppl. Rend. Circ. Palermo 46 (1997), 123-127. | MR

[12] Minči'c, S. M.: Ricci identities in the space of non-symmetric affine connection. Mat. Ves. 10 (1973), 161-172. | MR

[13] Minči'c, S. M.: New commutation formulas in the non-symmetric affine connection space. Publ. Inst. Math. (N. S) 22 (1977), 189-199. | MR

[14] Minči'c, S. M.: Independent curvature tensors and pseudotensors of spaces with non-symmetric affine connection. Coll. Math. Soc. János Bolyai 31 (1982), 445-460. | MR

[15] Minčić, S. M., Stanković, M. S., Velimirović, Lj. S.: Generalized Kählerian spaces. Filomat 15 (2001), 167-174. | MR

[16] Otsuki, T., Tasiro, Y.: On curves in Kählerian spaces. Math. J. Okayama Univ. 4 (1954), 57-78. | MR

[17] Prvanovi'c, M.: A note on holomorphically projective transformations in Kähler space. Tensor, N.S. 35 (1981), 99-104. | MR

[18] Radulovi'c, Zh.: Holomorphically-projective mappings of parabolically-Kählerian spaces. Math. Montisnigri 8 (1997), 159-184. | MR

[19] Shiha, M.: On the theory of holomorphically projective mappings of parabolically Kählerian spaces. In: Differential Geometry and Its Applications. Proc. 5th International Conference, Opava, August 24-28, 1992 Silesian University Opava (1993), 157-160. | MR | Zbl

[20] Sinyukov, N. S.: Geodesic Mappings of Riemannian Spaces. Nauka Moscow (1979), Russian. | MR | Zbl

[21] Stanković, M. S., Minčić, S. M., Velimirović, Lj. S.: On equitorsion holomorphically projective mappings of generalized Kählerian spaces. Czech. Math. J. 54(129) (2004), 701-715. | DOI | MR

[22] Vavříková, H., Mikeš, J., Pokorná, O., Starko, G.: On fundamental equations of almost geodesic mappings of type $\pi_2(e)$. Russ. Math. 51 (2007), 8-12. | DOI | MR

[23] Yano, K.: Differential Geometry of Complex and Almost Complex Spaces. Pergamon Press New York (1965). | MR

[24] Yano, K.: On complex conformal connections. Kodai Math. Semin. Rep. 26 (1975), 137-151. | DOI | MR | Zbl