Geodesic
On one class of three-webs with covariantly constant curvature and torsion tensors
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 85-91 
L. M. Pidzhakova. On one class of three-webs with covariantly constant curvature and torsion tensors. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 85-91. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a8/
@article{FPM_2010_16_2_a8,
     author = {L. M. Pidzhakova},
     title = {On one class of three-webs with covariantly constant curvature and torsion tensors},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {85--91},
     year = {2010},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a8/}
}
TY  - JOUR
AU  - L. M. Pidzhakova
TI  - On one class of three-webs with covariantly constant curvature and torsion tensors
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 85
EP  - 91
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a8/
LA  - ru
ID  - FPM_2010_16_2_a8
ER  - 
%0 Journal Article
%A L. M. Pidzhakova
%T On one class of three-webs with covariantly constant curvature and torsion tensors
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 85-91
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a8/
%G ru
%F FPM_2010_16_2_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

A special class of multidimensional three-webs $W^\nabla$ with covariantly constant curvature and torsion tensors is considered, the curvature tensor having the minimal rank. It is proved that there is a subfamily of adapted frames of the web $W^\nabla$ whose torsion tensor components are constant and the curvature tensor has a unique nonzero component. The structure equations of the webs of this class are found and some of their properties are described.

[1] Akivis M. A., “O tri-tkanyakh mnogomernykh poverkhnostei”, Itogi nauki i tekhn. Ser. Probl. geom. Tr. geom. sem., 2, 1969, 7–31 | MR | Zbl

[2] Akivis M. A., Shelekhov A. M., Mnogomernye tri-tkani i ikh prilozheniya, Tver, 2010

[3] Blyashke V., Vvedenie v geometriyu tkanei, GIFML, M., 1959

[4] Maltsev A. I., “Analiticheskie lupy”, Mat. sb., 36(78):3 (1955), 569–576 | MR | Zbl

[5] Pidzhakova L. M., “Tri-tkani s kovariantno postoyannymi tenzorami krivizny i krucheniya”, Itogi nauki i tekhn. Ser. Sovrem. mat. i eë pril. Temat. obz., 124, 2010, 176–190 | MR

[6] Trofimov V. V., Vvedenie v geometriyu mnogoobrazii s simmetriyami, Izd-vo Mosk. un-ta, M., 1989 | MR | Zbl

[7] Bol G., “Über zwei Kurvenscharen und eine Flachenschar”, Abh. Math. Sem. Univ. Hamburg, 9 (1932), 93–94 | DOI | MR | Zbl

[8] Chern S. S., “Eine Invariantentheorie der Dreigewebe aus $r$-dimensionalen Mannigfaltigkeiten in $\mathbf R_{2r}$”, Abh. Math. Sem. Univ. Hamburg, 11:1–2 (1936), 333–358 | MR | Zbl

[9] Shelekhov A. M., Pidzhakova L. M., “On three-webs with covariantly constant torsion and curvature tensors”, Webs and Quasigroups, 1998–1999, Tver State Univ., Tver, 1999, 92–103 | MR | Zbl