English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The goal of this paper is to describe Zermelo's navigation problem onRiemannian manifolds as a time-optimal control problem and give an efficientmethod in order to evaluate its control curvature. We will show that up tochange the Riemannian metric on the manifold the control curvature of Zermelo'sproblem has a simple to handle expression which naturally leads to ageneralization of the classical Gauss-Bonnet formula in an inequality. ThisGauss-Bonnet inequality enables to generalize for Zermelo's problems the E.Hopf theorem on flatness of Riemannian tori without conjugate points.

On Zermelo'-like problems: a Gauss-Bonnet inequality and a E. Hopf theorem