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

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International Electronic Journal of Geometry
Volume:15 Issue:1
The Scalar Curvature of a Projectively Invariant Metric Defined by the Kernel Function

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

Authors : Yadong WU, Hua ZHANG

Pages : 20-29

Doi:10.36890/iejg.1022605

View : 56 | Download : 12

Publication Date : 2022-04-30

Article Type : Research Paper

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 $insert ignore into journalissuearticles values(\Omega,\tau );$ has constant scalar curvature, then the convex domain is projectively equivalent to a ball.
Keywords : Scalar curvature, Fubini Pick invariant, kernel function

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