Abstract

In this paper we study the conjugate locus in convex manifolds. Our main tool is Jacobi fields, which we use to define a special coordinate system on the unit sphere of the tangent space; this provides a natural coordinate system to study and classify the singularities of the conjugate locus. We pay particular attention to 3-dimensional manifolds, and describe a novel method for determining conjugate points. We then make a study of a special case: the 3-dimensional (quadraxial) ellipsoid. We emphasise the similarities with the focal sets of 2-dimensional ellipsoids.

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 call

Disclaimer: 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.