Geodesic
Foliations associated with the structure of a~manifold over a~Grassman algebra of even degree exterior forms
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 83-86.

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

In this paper we consider a category of manifolds over the algebra of even degree exterior forms on $\mathbb R^N$. We give examples of the indicated manifolds. We explicitly find elements of the pseudogroup of differentiable transformations and demonstrate that on any differentiable manifold there exist affine foliations.
Keywords: Grassmann algebra, manifold over algebra
Mots-clés : foliation. 
@article{IVM_2012_1_a10,
     author = {S. Azarmi},
     title = {Foliations associated with the structure of a~manifold over {a~Grassman} algebra of even degree exterior forms},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--86},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_1_a10/}
}
TY  - JOUR
AU  - S. Azarmi
TI  - Foliations associated with the structure of a~manifold over a~Grassman algebra of even degree exterior forms
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2012
SP  - 83
EP  - 86
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2012_1_a10/
LA  - ru
ID  - IVM_2012_1_a10
ER  - 
%0 Journal Article
%A S. Azarmi
%T Foliations associated with the structure of a~manifold over a~Grassman algebra of even degree exterior forms
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2012
%P 83-86
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2012_1_a10/
%G ru
%F IVM_2012_1_a10
S. Azarmi. Foliations associated with the structure of a~manifold over a~Grassman algebra of even degree exterior forms. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 83-86. http://geodesic.mathdoc.fr/item/IVM_2012_1_a10/

[1] Azarmi S., “Mnogoobraziya nad grassmanovymi algebrami”, Lobachevskie chteniya–2009, Materialy 8-i molodezhnoi nauchn. shk.-konf. (Kazan, 1–6 noyabrya 2009 g.), Tr. Matem. tsentra im. N. I. Lobachevskogo, 39, Kazansk. matem. ob-vo, Kazan, 2009, 116–118

[2] Pilch K., Jadczyk A., “Superspace and supersymmetries”, Comm. Math. Phys., 78:3 (1980), 373–390 | MR

[3] Vladimirov V. S., Volovich I. V., “Superanaliz. I. Differentsialnoe ischislenie”, Teor. i matem. fizika, 59:1 (1984), 3–27 | MR | Zbl

[4] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Prostranstva nad algebrami, Izd-vo Kazansk. un-ta, Kazan, 1985 | MR

[5] Shurygin V. V., “Rassloeniya strui kak mnogoobraziya nad algebrami”, Itogi nauki i tekhn. Ser. Probl. geom., 19, VINITI, M., 1987, 3–22 | MR | Zbl

[6] Vishnevskii V. V., “Mnogoobraziya nad plyuralnymi chislami i polukasatelnye struktury”, Itogi nauki i tekhn. Ser. Probl. geom., 20, VINITI, M., 1988, 35–74 | MR

[7] Shurygin V. V., “Mnogoobraziya nad algebrami i ikh primenenie v geometrii rassloenii strui”, UMN, 48:2 (1993), 75–106 | MR | Zbl