The problem of constructive equivalence in differential geometry
Journal Article
·
· Sbornik. Mathematics
- International Center 'Sophus Lie', Moscow (Russian Federation)
The present paper is devoted to the algorithmic construction of diffeomorphisms establishing the equivalence of geometric structures. For structures of finite type the problem reduces to integration of completely integrable distributions with a known symmetry algebra and further to integration of Maurer-Cartan forms. We develop algorithms that reduce this problem to integration of closed 1-forms and equations of Lie type that are characterized by the fact that they admit a non-linear superposition principle. As an application we consider the problem of constructive equivalence for the structures of absolute parallelism and for the transitive Lie algebras of vector fields on manifolds.
- OSTI ID:
- 21202937
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 5 Vol. 191; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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