The Scalar Curvature of a Projectively Invariant Metric Defined by the Kernel Function

Year 2022, Volume: 15 Issue: 1, 20 - 29, 30.04.2022

Yadong Wu , Hua Zhang

https://doi.org/10.36890/iejg.1022605

Abstract

Considering a projectively invariant metric $\tau$ defined by the kernel function on a strongly convex bounded domain $\Omega\subset\mathbb{R}^n$,
we study the asymptotic expansion of the scalar curvature with respect to the distance function, and use the Fubini-Pick invariant to describe the second term in the expansion. This asymptotic expansion implies that if $n\geq 3$ and $(\Omega,\tau )$ has constant scalar curvature, then the convex domain is projectively equivalent to a ball.

Keywords

Scalar curvature, Fubini-Pick invariant, kernel function

Supporting Institution

NSFC

Project Number

12061036

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