UC Santa Cruz

We study unparametrized conformal geodesics, or called conformal circles, and study local diffeomorphisms mapping conformal geodesics to conformal geodesics in pseudo-Riemannian conformal manifolds. We show that such local diffeomorphisms are conformal local diffeomorphisms. Our result extends the result of Yano and Tomonaga. We also present a holographic interpretation for our result on Poincaré-Einstein manifolds. The proofs take suitable variations of conformal geodesics.