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Calculus of odd base forms on differential manifolds. (English) Zbl 0618.58001

Folia Fac. Sci. Nat. Univ. Purkynianae Brun. Phys. 24, No. 7, 64 p. (1983).
The odd base forms occur in a natural way in the global variational calculus on manifolds. This booklet is a detailed and elementary account of the basic definitions, constructions and properties of these objects, including integration and the Stokes formula. Explicit coordinate formulas are given and the prerequisites of Lebesgue integration theory are recalled. This work is intended for a wide audience of mathematicians and mathematical physicists, and is adapted to applications in geometry, calculus of variations and mathematical physics.

MSC:

58A10 Differential forms in global analysis
58-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis
58E99 Variational problems in infinite-dimensional spaces