Siberian Federal University

In 1907, H. Poincar´e 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 Poincar´e’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, Poincar´e’s methods can compete with ´ E. 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.