Modern geometry. Methods and applications. Textbook. (Sovremennaya geometriya. Metody i prilozheniya. Uchebnoe posobie). 2nd ed., rev. (Russian) Zbl 0601.53001

Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.

Moskva: ”Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 760 p. R. 1.90 (1986).

[For a review of the first edition (1979), see Zbl 0433.53001.]
The revision consists in the following: (1) The exposition of the Hamilton formalism is modified, a systematic exposition of the infinite- dimensional Hamilton formalism (for field theory) is included; (2) integration over noncommutative variables is included; (3) the exposition of multidimensional variational problems is extended, including the problem of the energy of the gravitational field; (4) a heuristic physical motivation is given before the formal definition of a manifold is introduced.

Reviewer: V.Ya.Kreinovich

MSC:

53-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
51-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry
15-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
58-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis

Keywords:

Hamilton formalism