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.

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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 
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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/

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