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This book is expository and is in Russian (sample English translation of two pages is given). It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear different notions of curvature, which distinguish given geometry from the ordinary one. Direct elementary definitions of these notions are presented. The book is accessible for students familiar with analysis of several variables, and could be an interesting easy reading for professional mathematicians. The material is presented as a sequence of problems, which is peculiar not only to Zen monasteries but also to serious mathematical education.
This paper has been withdrawn by the authors due to the fact that the webs considered in the paper are ``Veronese-like webs which are different from Veronese webs.
This is a preliminary version of our book. It goes up to the definition of dimension, which is about 30% of the material we plan to include. If you use it as a reference, do not forget to include the version number since the numbering will be changed.
Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in the equivari
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the transformation group p
We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system leads to