Geodesic
Examples from the calculus of variations. III. Legendre and Jacobi conditions
Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 93-111.

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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.
DOI : 10.21136/MB.2001.133926
Classification : 49-01, 49K10, 49K15, 49K27, 58A10, 58E30
Keywords: Legendre condition; Jacobi condition; Poincaré-Cartan form; Lagrange problem; degenerate variational integral 
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Chrastina, Jan. Examples from the calculus of variations. III. Legendre and Jacobi conditions. Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 93-111. doi : 10.21136/MB.2001.133926. http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.133926/

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