Basic differential geometry as a sequence of interesting problems

Details Basic differential geometry as a sequence of interesting problems Basic differential geometry as a sequence of interesting problems

2008-01-10

arxiv.org/abs/0801.1568v3

MCCME, Moscow, 2008

Mathematics

Differential Geometry

51 pages, 9 figures, English version expanded, misprints corrected

Scientific paper

This paper is purely expositional 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 paper is accessible for students familiar with analysis of several variables, and could be an interesting easy reading for mature mathematicians. The material is presented as a sequence of problems, which is peculiar not only to Zen monasteries but also to elite mathematical education (at least in Russia).

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