Geodesic
Fedosov supermanifolds
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 202-227 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the properties of the symplectic curvature tensor on supermanifolds. Using the method of normal coordinates, we establish higher-order relations between affine extensions of the curvature tensor and of the symplectic structure tensor. We find a generating function for higher-order relations.
Keywords: supermanifold, tensor field, covariant derivative, symplectic curvature tensor. 
@article{TMF_2006_149_2_a3,
     author = {P. M. Lavrov and O. V. Radchenko},
     title = {Fedosov supermanifolds},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {202--227},
     year = {2006},
     volume = {149},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a3/}
}
TY  - JOUR
AU  - P. M. Lavrov
AU  - O. V. Radchenko
TI  - Fedosov supermanifolds
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 202
EP  - 227
VL  - 149
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a3/
LA  - ru
ID  - TMF_2006_149_2_a3
ER  - 
%0 Journal Article
%A P. M. Lavrov
%A O. V. Radchenko
%T Fedosov supermanifolds
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 202-227
%V 149
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a3/
%G ru
%F TMF_2006_149_2_a3
P. M. Lavrov; O. V. Radchenko. Fedosov supermanifolds. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 202-227. http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a3/

[1] B. V. Fedosov, J. Diff. Geom., 40 (1994), 213 ; Deformation Quantization and Index Theory, Akademie Verlag, Berlin, 1996 | DOI | MR | Zbl | MR | Zbl

[2] I. Gelfand, V. Retakh, M. Shubin, Advan. Math., 136 (1998), 104 | DOI | MR | Zbl

[3] F. A. Berezin, YaF, 29 (1979), 1670 ; 30 (1979), 1168 ; Введение в алгебру и анализ с антикоммутирующими переменными, МГУ, М., 1983 | MR | Zbl | MR | Zbl | MR | Zbl

[4] D. A. Leites, UMN, 35:1 (1980), 3 ; B. DeWitt, Supermanifolds, Cambridge University Press, Cambridge, 1992 | MR | Zbl | MR | Zbl

[5] I. A. Batalin, G. A. Vilkovisky, Phys. Lett. B, 102 (1981), 27 ; Phys. Rev. D, 28 (1983), 2567 | DOI | MR | DOI | MR

[6] E. Witten, Mod. Phys. Lett. A, 5 (1990), 487 ; O. M. Khudaverdian, J. Math. Phys., 32 (1991), 1934 | DOI | MR | Zbl | DOI | MR | Zbl

[7] I. A. Batalin, I. V. Tyutin, Nucl. Phys. B, 345 (1990), 645 ; B. Geyer, P. Lavrov, Int. J. Mod. Phys. A, 19 (2004), 1639 | DOI | MR | DOI | MR | Zbl

[8] B. S. Devitt, Dinamicheskaya teoriya grupp i polei, Nauka, M., 1987 | MR | Zbl

[9] D. M. Gitman, I. V. Tyutin, Kanonicheskoe kvantovanie polei so svyazyami, Nauka, M., 1986 | MR | Zbl

[10] A. S. Mischenko, A. T. Fomenko, Kurs differentsialnoi geometrii i topologii, Izd-vo MGU, M., 1980 | MR | Zbl

[11] B. Geyer, P. Lavrov, Int. J. Mod. Phys. A, 20 (2005), 2179 | DOI | MR | Zbl