German Fedorovich Laptev, his unique method, achievements, and modern contribution. On the 100th anniversary of the birth of our teacher
type: Item
instance of: scholarly article
title: German Fedorovich Laptev, his unique method, achievements, and modern contribution. On the 100th anniversary of the birth of our teacher
zbMATH Open document ID: 1221.53002
author: Leonid Evgen'evich Evtushik
published in: Journal of Mathematical Sciences (New York)
publication date: 2011-06-30T00:00:00Z
review text: 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.
reviewed by: Yuriy V. Rogovchenko
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 01A70
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57N16
zbMATH DE Number: 5915278
zbMATH Keywords: German Fedorovich Laptev
zbMATH Keywords: group-theoretic methods
zbMATH Keywords: Lie group structural differential forms
zbMATH Keywords: Lie group representation spaces
zbMATH Keywords: smooth manifolds
zbMATH Keywords: differential structures
MaRDI profile type: Publication
full work available at URL: s10958-010-0048-1
OpenAlex ID: W2037079256
cites work: Q3125476
cites work: Invariant description of higher order ordinary differential system
cites work: Q4766274
cites work: Differential-geometric structures on manifolds
cites work: Q4319049
DOI: 10.1007/S10958-010-0048-1
description: scientific article; zbMATH DE number 5915278