The Programm of Poincaré as Alternative to Klein's Programm (to Centenary of Publication)
Valery K. Beloshapka
Faculty of Mechanics and Mathematics, Moscow State University
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.
$G$-strucrure, pseudogroup of transformations, Lie group, Lie algebra, real submanifold, model surface, moduli space.
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Valery K. Beloshapka, “The Programm of Poincaré as Alternative to Klein's Programm (to Centenary of Publication)”, J. Sib. Fed. Univ. Math. Phys., 1:1 (2008), 63–67
Citation in format AMSBIB
\paper The Programm of Poincar\'e as Alternative to Klein's Programm (to Centenary of Publication)
\jour J. Sib. Fed. Univ. Math. Phys.
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