We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 30 May 2025
We discuss various recent results related to the inverse problem of determining a unitary connection from its parallel transport along geodesics.
Let (M, g) be a compact oriented Riemannian manifold with smooth boundary, and let SM = {(x, v) ∈ TM : |v| =1} be the unit tangent bundle with canonical projection π : SM → M. The geodesics going from ∂M into M can be parametrized by the set ∂+(SM) = {(x, v) 2 SM : x ∈ ∂M, (u, v) ≤ 0}, where is the outer unit normal vector to ∂M. For any (x, v) ∈ SM we let t →γ(t, x, v) be the geodesic starting from x in direction v. We assume that (M, g) is nontrapping, which means that the time τ( x; v) when the geodesic γ(t, x, v) exits M is finite for each (x, v) ∈ SM. The scattering relation
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
