German Fedorovich Laptev, his unique method, achievements, and modern contribution. On the 100th anniversary of the birth of our teacher
This article is written on the occasion of the 100th anniversary of the birth of Professor German Fedorovich Laptev, known as a creator of universal invariant group-theoretic methods for studying differential-geometric object fields in spaces of representations of all possible Lie groups and in submanifolds of these spaces on the basis of Lie group structural differential forms and Lie group representation spaces. After a brief biographical sketch, the author overviews the development of Laptev's ideas in recent work of his colleagues and former students focusing attention on differential-algebraic techniques for invariant description of higher-order geometric structures on smooth manifolds, geometry of reducible differential systems \(f^{p+1} :T^{p}\left( V_{n}\right) \rightarrow T^{p+1}\left( V_{n}\right) \) and invariant description of second-order Lagrangians of metric type.
scientific article; zbMATH DE number 5915278