We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail -dimensional surfaces in contact manifolds of dimension . We show that in this case minimal surfaces are projections of a special class of -dimensional surfaces...
We study minimal surfaces in sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called area functional associated with the canonical area form. We derive the intrinsic equation in the general case and then consider in greater detail -dimensional surfaces in contact manifolds of dimension . We show that in this case minimal surfaces are projections of a special class of -dimensional surfaces in the horizontal...
The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...
The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...
The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on (3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S associated to the dynamics...
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