The projective symplectic geometry of higher order variational problems: Minimality conditions

Carlos  Durán; Diego  Otero

doi:10.3934/jgm.2016009

Article Contents

2016, Volume 8, Issue 3: 305-322. Doi: 10.3934/jgm.2016009

This issue Previous Article Shape analysis on Lie groups with applications in computer animation Next Article Minimal geodesics on GL(n) for left-invariant, right-O(n)-invariant Riemannian metrics

The projective symplectic geometry of higher order variational problems: Minimality conditions

Carlos Durán^1, and
Diego Otero^1,

1.
Departamento de Matemática, UFPR, Setor de Ciências Exatas, Centro Politécnico, Caixa Postal 019081, CEP 81531-990, Curitiba

Received: October 2015

Revised: April 2016

Published: September 2016

Abstract / Introduction Related Papers Cited by

Abstract

We associate curves of isotropic, Lagrangian and coisotropic subspaces to higher order, one parameter variational problems. Minimality and conjugacy properties of extremals are described in terms self-intersections of these curves.

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Mathematics Subject Classification: Primary: 49K05; Secondary: 53D12.

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