Conformal Circles and Local Diffeomorphisms

2022/10/12 by Kuo, Tzu-Mo
#53 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2210.05864

Abstract

We study unparametrized conformal circles, or called conformal geodesics, study diffeomorphisms mapping conformal circles to conformal circles 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 circles.

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