Geodesic
$r$-tuple almost product structures
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 81-93.

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

A generalization of an almost product structure and an almost complex structure on smooth manifolds is constructed. The set of tensor differential invariants of type $(2,1)$ and the set of the differential 2-forms for such structures are constructed. We show how these tensor invariants can be used to solve the classification problem for Monge–Ampère equations and Jacobi equations. 
@article{FPM_2010_16_1_a6,
     author = {A. G. Kushner},
     title = {$r$-tuple almost product structures},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {81--93},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a6/}
}
TY  - JOUR
AU  - A. G. Kushner
TI  - $r$-tuple almost product structures
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 81
EP  - 93
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a6/
LA  - ru
ID  - FPM_2010_16_1_a6
ER  - 
%0 Journal Article
%A A. G. Kushner
%T $r$-tuple almost product structures
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 81-93
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a6/
%G ru
%F FPM_2010_16_1_a6
A. G. Kushner. $r$-tuple almost product structures. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 81-93. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a6/

[1] Kushner A. G., “Kontaktnaya linearizatsiya nevyrozhdennykh uravnenii Monzha–Ampera”, Izv. vyssh. uchebn. zaved. Matematika, 2008, no. 4, 43–58 | MR | Zbl

[2] Cotton E., “Sur les invariants différentiels de quelques équations linearies aux dérivées partielles du second ordre”, Ann. Sci. École Norm. Sup., 17 (1900), 211–244 | MR | Zbl

[3] Kushner A. G., “Almost product structures and Monge–Ampère equations”, Lobachevskii J. Math., 23 (2006), 151–181 http://ljm.ksu.ru | MR | Zbl

[4] Kushner A. G., “A contact linearization problem for Monge–Ampère equations and Laplace invariants”, Acta Appl. Math., 101:1–3 (2008), 177–189 | DOI | MR | Zbl

[5] Kushner A. G., “Classification of Monge–Ampère equations”, Differential Equations: Geometry, Symmetries and Integrability. The Abel Symposium 2008, Proc. of the Fifth Abel Symposium on Differential Equations: Geometry, Symmetries and Integrability (June 18–21, 2008, Tromsø, Norway), eds. B. Kruglikov, V. Lychagin, E. Straume, Springer, Berlin, 2009, 223–256 | DOI | MR | Zbl

[6] Kushner A. G., “On contact equivalence of Monge–Ampère equations to linear equations with constant coefficients”, Acta Appl. Math., 109:1 (2010), 197–210 | DOI | MR | Zbl

[7] Kushner A. G., Lychagin V. V., Rubtsov V. N., Contact Geometry and Nonlinear Differential Equations, Encyclopedia of Mathematics and Its Applications, 101, Cambridge Univ. Press, Cambridge, 2007 | MR | Zbl

[8] Laplace P. S., “Recherches sur le calcul intégrals aux différences partielles”, Mémoires de l'Académie royale des Sciences de Paris, 1773, 341–401; Oeuvres complètes, 9, Gauthier-Villars, Paris, 1893, 3–68; English translation: New York, 1966

[9] Lie S., “Über einige partielle Differential-Gleichungen zweiter Orduung”, Math. Ann., 5 (1872), 209–256 | DOI | MR

[10] Lie S., “Begrundung einer Invarianten-Theorie der Beruhrungs-Transformationen”, Math. Ann., 8 (1874), 215–303 | DOI | MR

[11] Lychagin V. V., Lectures on Geometry of Differential Equations, La Sapienza, Rome, 1993