2004/04/12 by L. I. Petrova, Petrova, L. I.
Agricultural and Biological Sciences · #Advanced Scientific Research Methods #Differential Geometry (math.DG) #FOS: Mathematics #LaTex2e
paper · pdf · doi:10.48550/arxiv.math/0404232
openalex publication_date 2004/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The using of skew-symmetric differential forms enables one to reveal a mechanism of forming differential-geometrical structures as well. To do this, it is necessary to consider the skew-symmetric differential forms whose basis, unlike to the case of exterior differential forms, are manifolds with unclosed metric forms. Such differential forms possess the evolutionary properties. They can generate closed differential forms, which correspond to the differential-geometrical structures.