Holomorphically projective mappings of compact semisymmetric manifolds

Raad J. K. al Lami

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)

  • Volume: 49, Issue: 1, page 49-53
  • ISSN: 0231-9721

Abstract

top
In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces A n onto (pseudo-) Kählerian spaces K ¯ n . We proved that in this case space A n is holomorphically projective flat and K ¯ n is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.

How to cite

top

al Lami, Raad J. K.. "Holomorphically projective mappings of compact semisymmetric manifolds." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.1 (2010): 49-53. <http://eudml.org/doc/116476>.

@article{alLami2010,
abstract = {In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces $A_n$ onto (pseudo-) Kählerian spaces $\bar\{K\}_n$. We proved that in this case space $A_n$ is holomorphically projective flat and $\bar\{K\}_n$ is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.},
author = {al Lami, Raad J. K.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Holomorphically projective mapping; equiaffine space; affine-connected space; semisymmetric space; Riemannian space; Kählerian space; holomorphically projective mapping; equiaffine space; affine-connected space; semisymmetric space; Riemannian space; Kählerian space},
language = {eng},
number = {1},
pages = {49-53},
publisher = {Palacký University Olomouc},
title = {Holomorphically projective mappings of compact semisymmetric manifolds},
url = {http://eudml.org/doc/116476},
volume = {49},
year = {2010},
}

TY - JOUR
AU - al Lami, Raad J. K.
TI - Holomorphically projective mappings of compact semisymmetric manifolds
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 1
SP - 49
EP - 53
AB - In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces $A_n$ onto (pseudo-) Kählerian spaces $\bar{K}_n$. We proved that in this case space $A_n$ is holomorphically projective flat and $\bar{K}_n$ is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.
LA - eng
KW - Holomorphically projective mapping; equiaffine space; affine-connected space; semisymmetric space; Riemannian space; Kählerian space; holomorphically projective mapping; equiaffine space; affine-connected space; semisymmetric space; Riemannian space; Kählerian space
UR - http://eudml.org/doc/116476
ER -

References

top
  1. Beklemishev, D. V., Differential geometry of spaces with almost complex structure, Geometria. Itogi Nauki i Tekhn., All-Union Inst. for Sci. and Techn. Information (VINITI), Akad. Nauk SSSR, Moscow, (1965), 165–212. (1965) MR0192434
  2. Boeckx, E., Kowalski, O., Vanhecke, L., Riemannian manifolds of conullity two, World Sci., 1996. (1996) Zbl0904.53006MR1462887
  3. Domashev, V. V., Mikeš, J., 10.1007/BF01153160, Math. Notes 23 (1978), 160–163, transl. from Mat. Zametki 23, 2 (1978), 297–304. (1978) MR0492674DOI10.1007/BF01153160
  4. Kurbatova, I. N., HP-mappings of H-spaces, Ukr. Geom. Sb., Kharkov 27 (1984), 75–82. (1984) Zbl0571.58006MR0767421
  5. Lakomá, L., Jukl, M., The decomposition of tensor spaces with almost complex structure, Suppl. Rend. Circ. Mat. (Palermo) 72, II (2004), 145–150. (2004) Zbl1064.53015MR2069402
  6. Al Lamy, 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. (2006) MR2322415
  7. Mikeš, J., Geodesic mappings onto semisymmetric spaces, Russ. Math. 38, 2 (1994), 35–41, transl. from Izv. Vyssh. Uchebn. Zaved., Mat. 381, 2 (1994), 37–43. (1994) MR1302090
  8. Mikeš, J., On special F-planar mappings of affine-connected spaces, Vestn. Mosk. Univ. 3 (1994), 18–24. (1994) MR1315721
  9. Mikeš, J., 10.1007/BF02365193, J. Math. Sci., New York 78, 3 (1996), 311–333. (1996) MR1384327DOI10.1007/BF02365193
  10. Mikeš, J., Holomorphically projective mappings and their generalizations, J. Math. Sci., New York 89, 3 (1998), 1334–1353. (1998) MR1619720
  11. Mikeš, J., Chodorová, M., On concircular and torse-forming vector fields on compact manifolds, Acta Acad. Paedagog. Nyregyházi., Mat.-Inform. Közl. (2010). (2010) Zbl1240.53028MR2754424
  12. Mikeš, J., Pokorná, O., On holomorphically projective mappings onto Kählerian spaces, Suppl. Rend. Circ. Mat. (Palermo) 69, II (2002), 181–186. (2002) Zbl1023.53015MR1972433
  13. 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, transl. from Izv. Vyssh. Uchebn., Mat 1996, 10(413), 30–35. (1996) MR1447076
  14. Mikeš, J., Sinyukov, N. S., On quasiplanar mappings of spaces of affine connection, Sov. Math. 27, 1 (1983), 63–70, transl. from Izv. Vyssh. Uchebn. Zaved., Mat., 1983, 1(248), 55–61. (1983) MR0694014
  15. Mikeš, J., Starko, G. A., K-concircular vector fields and holomorphically projective mappings on Kählerian spaces, Circ. Mat. di Palermo, Suppl. Rend. Circ. Mat. (Palermo) 46, II (1997), 123–127. (1997) MR1469028
  16. Mikeš, J., Vanžurová, A., Hinterleitner, I., Geodesic Mappings and some Generalizations, Palacký Univ. Publ., Olomouc, 2009. (2009) Zbl1222.53002MR2682926
  17. Otsuki, T., Tashiro, Y., On curves in Kaehlerian spaces, Math. J. Okayama Univ. 4 (1954), 57–78. (1954) Zbl0057.14101MR0066024
  18. Petrov, A. Z., Simulation of physical fields, In: Gravitation and the Theory of Relativity, 4–5, Kazan’ State Univ., Kazan, 1968, 7–21. (1968) MR0285249
  19. Sakaguchi, T., On the holomorphically projective correspondence between Kählerian spaces preserving complex structure, Hokkaido Math. J. 3 (1974), 203–212. (1974) Zbl0305.53024MR0370411
  20. Sinyukov, N. S., Geodesic mappings of Riemannian spaces, Nauka, Moscow, 1979. (1979) Zbl0637.53020MR0552022
  21. Sinyukov, N. S., 10.1007/BF01084672, J. Sov. Math. 25 (1984), 1235–1249. (1984) DOI10.1007/BF01084672
  22. Sobchuk, V. S., Mikeš, J., Pokorná, O., On almost geodesic mappings π 2 between semisymmetric Riemannian spaces, Novi Sad J. Math. 29, 3 (1999), 309–312. (1999) MR1771008
  23. Yano, K., Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, Oxford–London–New York–Paris–Frankfurt, 1965. (1965) Zbl0127.12405MR0187181
  24. Yano, K., Bochner, S., Curvature and Betti Numbers, Annals of Mathematics Studies 32, Princeton University Press, Princeton, 1953. (1953) Zbl0051.39402MR0062505

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.