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Title: Examples from the calculus of variations. III. Legendre and Jacobi conditions (English)
Author: Chrastina, Jan
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 126
Issue: 1
Year: 2001
Pages: 93-111
Summary lang: English
Category: math
Summary: We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II. (English)
Keyword: Legendre condition
Keyword: Jacobi condition
Keyword: Poincaré-Cartan form
Keyword: Lagrange problem
Keyword: degenerate variational integral
MSC: 49-01
MSC: 49K10
MSC: 49K15
MSC: 49K27
MSC: 58A10
MSC: 58E30
idZBL: Zbl 0980.49024
idMR: MR1826474
DOI: 10.21136/MB.2001.133926
Date available: 2009-09-24T21:47:48Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] J. Chrastina: Examples from the calculus of variations I. Nondegenerate problems.Math. Bohem. 125 (2000), 55–76. Zbl 0968.49001, MR 1752079
Reference: [2] W. Fulton, J. Harris: Representation Theory.Graduate Texts in Mathematics 129, Springer, 1996. MR 1153249


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