Geodesic
The Programm of Poincar\'e as Alternative to Klein's Programm (to Centenary of Publication)
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 1, pp. 63-67

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

In 1907, H. Poincaré suggested a new approach to infinite-dimensional geometry. In a sense, his approach is dual to the famous Klein's program. The first step of Poincaré's approach is to single out a canonical object and then to consider the symmetry group of the object, whereas the Klein's program is the passage from a prescribed structure group to objects. Now, a century later, Poincaré's methods can compete with É. Cartan's $G$-structure reduction. In the present paper, this competition is illustrated by some results in the geometry of real submanifolds of the complex space.
Mots-clés : $G$-strucrure, pseudogroup of transformations, Lie group, moduli space.
Keywords: Lie algebra, real submanifold, model surface 
@article{JSFU_2008_1_1_a6,
     author = {Valery K. Beloshapka},
     title = {The {Programm} of {Poincar\'e} as {Alternative} to {Klein's} {Programm} (to {Centenary} of {Publication)}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {63--67},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a6/}
}
TY  - JOUR
AU  - Valery K. Beloshapka
TI  - The Programm of Poincar\'e as Alternative to Klein's Programm (to Centenary of Publication)
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2008
SP  - 63
EP  - 67
VL  - 1
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a6/
LA  - ru
ID  - JSFU_2008_1_1_a6
ER  - 
%0 Journal Article
%A Valery K. Beloshapka
%T The Programm of Poincar\'e as Alternative to Klein's Programm (to Centenary of Publication)
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2008
%P 63-67
%V 1
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a6/
%G ru
%F JSFU_2008_1_1_a6
Valery K. Beloshapka. The Programm of Poincar\'e as Alternative to Klein's Programm (to Centenary of Publication). Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 1, pp. 63-67. http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a6/