Abstract
We formulate a brachistochrone problem in Lorentzian geometry and we prove a variational principle valid for brachistochrones in stationary manifolds. This variational principle is stated in terms of geodesics in a suitable sub-Riemannian structure on ℳ. Moreover, we prove the regularity of the solutions of our variational problem and we determine a differential equation satisfied by the brachistochrones. Some explicit examples are computed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
