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J. Sib. Fed. Univ. Math. Phys., 2008, Volume 1, Issue 1, Pages 63–67 (Mi jsfu7)  

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

Abstract: 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.

Keywords: $G$-strucrure, pseudogroup of transformations, Lie group, Lie algebra, real submanifold, model surface, moduli space.

Full text: PDF file (273 kB)
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UDC: 517.55
Received: 01.09.2007
Accepted: 10.10.2007

Citation: 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
\Bibitem{Bel08}
\by Valery~K.~Beloshapka
\paper The Programm of Poincar\'e as Alternative to Klein's Programm (to Centenary of Publication)
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2008
\vol 1
\issue 1
\pages 63--67
\mathnet{http://mi.mathnet.ru/jsfu7}


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