Application of codimension one foliation in Zermelo's problem on Riemannian manifolds

DOI10.1016/J.DIFGEO.2014.04.007zbMath1334.53010OpenAlexW2043436636WikidataQ115356266 ScholiaQ115356266MaRDI QIDQ2351006

Piotr Kopacz

Publication date: 26 June 2015

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2014.04.007

zbMATH Keywords

Euler-Lagrange equationsRiemannian manifoldfoliationZermelo navigationpath optimization

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Foliations (differential geometric aspects) (53C12) Applications of local differential geometry to the sciences (53B50) Foliations in differential topology; geometric theory (57R30) Local Riemannian geometry (53B20) Differential invariants (local theory), geometric objects (53A55)

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Cites Work

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• Time optimal Zermelo's navigation problem with moving and fixed obstacles
• Deforming metrics of foliations
• Riemannian foliations. With appendices by G. Cairns, Y. Carrière, E. Ghys, E. Salem, V. Sergiescu
• Zermelo navigation on Riemannian manifolds
• Foliated and associated geometric structures on foliated manifolds
• Über das Navigationsproblem bei ruhender oder veränderlicher Windverteilung

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