Metric of special 2F-flat Riemannian spaces

Raad J. K. al Lami

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2005)

  • Volume: 44, Issue: 1, page 7-11
  • ISSN: 0231-9721

Abstract

top
In this paper we find the metric in an explicit shape of special 2 F -flat Riemannian spaces V n , i.e. spaces, which are 2 F -planar mapped on flat spaces. In this case it is supposed, that F is the cubic structure: F 3 = I .

How to cite

top

al Lami, Raad J. K.. "Metric of special 2F-flat Riemannian spaces." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 44.1 (2005): 7-11. <http://eudml.org/doc/32446>.

@article{alLami2005,
abstract = {In this paper we find the metric in an explicit shape of special $2F$-flat Riemannian spaces $V_n$, i.e. spaces, which are $2F$-planar mapped on flat spaces. In this case it is supposed, that $F$ is the cubic structure: $F^3=I$.},
author = {al Lami, Raad J. K.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {$2F$-flat (pseudo-)Riemannian spaces; $2F$-planar mapping; cubic structure},
language = {eng},
number = {1},
pages = {7-11},
publisher = {Palacký University Olomouc},
title = {Metric of special 2F-flat Riemannian spaces},
url = {http://eudml.org/doc/32446},
volume = {44},
year = {2005},
}

TY - JOUR
AU - al Lami, Raad J. K.
TI - Metric of special 2F-flat Riemannian spaces
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2005
PB - Palacký University Olomouc
VL - 44
IS - 1
SP - 7
EP - 11
AB - In this paper we find the metric in an explicit shape of special $2F$-flat Riemannian spaces $V_n$, i.e. spaces, which are $2F$-planar mapped on flat spaces. In this case it is supposed, that $F$ is the cubic structure: $F^3=I$.
LA - eng
KW - $2F$-flat (pseudo-)Riemannian spaces; $2F$-planar mapping; cubic structure
UR - http://eudml.org/doc/32446
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. Eisenhart L. P.: Riemannian Geometry., Princenton Univ. Press, , 1926. (1926) MR1487892
  3. Kurbatova I. N., HP-mappings of H-spaces, Ukr. Geom. Sb., Kharkov, 27 (1984), 75–82. (1984) Zbl0571.58006MR0767421
  4. Al Lamy R. J., About 2F-plane mappings of affine connection spaces, Coll. on Diff. Geom., Eger (Hungary), 1989, 20–25. (1989) 
  5. Al Lamy R. J., Kurbatova I. N., Invariant geometric objects of 2F-planar mappings of affine connection spaces and Riemannian spaces with affine structure of III order, Dep. of UkrNIINTI (Kiev), 1990, No. 1004Uk90, 51p. (1990) 
  6. Al Lamy R. J., Mikeš J., Škodová M., On linearly p F -planar mappings, Diff. Geom. and its Appl. Proc. Conf. Prague, 2004, Charles Univ., Prague (Czech Rep.), 2005, 347–353. Zbl1114.53012
  7. J. Mikeš, On special F-planar mappings of affine-connected spaces, Vestn. Mosk. Univ., 1994, 3, 18–24. (1994) MR1315721
  8. Mikeš J., Geodesic mappings of affine-connected and Riemannian spaces, J. Math. Sci., New York, 78, 3 (1996), 311–333. (1996) Zbl0866.53028MR1384327
  9. Mikeš J., Holomorphically projective mappings and their generalizations, J. Math. Sci., New York, 89, 3 (1998), 1334–1353. (1998) Zbl0983.53013MR1619720
  10. Mikeš J., Pokorná O., On holomorphically projective mappings onto Kählerian spaces, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, (2002), 181–186. Zbl1023.53015MR1972433
  11. Mikeš J., Sinyukov N. S., On quasiplanar mappings of spaces of affine connection, Sov. Math. 27, 1 (1983), 63–70; translation from Izv. Vyssh. Uchebn. Zaved., Mat., 248, 1 (1983), 55–61. (1983) Zbl0526.53013MR0694014
  12. Petrov A. Z.: New Method in General Relativity Theory., Nauka, Moscow, , 1966. (1966) MR0207365
  13. Petrov A. Z., Simulation of physical fields, In: Gravitation and the Theory of Relativity, Vol. 4–5, Kazan’ State Univ., Kazan, 1968, 7–21. (1968) MR0285249
  14. Shirokov P. A.: Selected Work in Geometry., Kazan State Univ. Press, Kazan, , 1966. (1966) 
  15. Sinyukov N. S.: Geodesic Mappings of Riemannian Spaces., Nauka, Moscow, , 1979. (1979) MR0552022
  16. Sinyukov N. S., Almost geodesic mappings of affinely connected and Riemannian spaces, J. Sov. Math. 25 (1984), 1235–1249. (1984) 
  17. Škodová M., Mikeš J., Pokorná O., On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces, Circ. Mat. di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 75, (2005), 309–316. Zbl1109.53019MR2152369
  18. Yano K.: Differential Geometry on Complex, Almost Complex Spaces., Pergamon Press, Oxford–London–New York–Paris–Frankfurt, , XII, 1965, 323p. (1965) MR0187181

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.