Two Kazdan-Warner-type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric

Bin Guo; Zheng Chao Han; Haizhong Li

doi:10.2140/pjm.2011.251.257

Two Kazdan-Warner-type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric

Bin Guo, Zheng Chao Han, Haizhong Li

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove two Kazdan-Warner-type identities involving the renormalized volume coefficients v^2k of a Riemannian manifold (Mⁿ, g), the Gauss- Bonnet curvature G2r, and a conformal Killing vector field on (Mⁿ, g). In the case when the Riemannian manifold is locally conformally flat, we find and our results reduce to earlier ones established by Viaclovsky in 2000 and the second author in 2006.

Original language	English (US)
Pages (from-to)	257-268
Number of pages	12
Journal	Pacific Journal of Mathematics
Volume	251
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2011.251.257
State	Published - 2011

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Conformal transformation
Gauss-Bonnet curvatures
Kazdan-Warner
Locally conformally flat
Renormalized volume coefficients
v curvature
σ curvature

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10.2140/pjm.2011.251.257

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title = "Two Kazdan-Warner-type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric",

abstract = "We prove two Kazdan-Warner-type identities involving the renormalized volume coefficients v2k of a Riemannian manifold (Mn, g), the Gauss- Bonnet curvature G2r, and a conformal Killing vector field on (Mn, g). In the case when the Riemannian manifold is locally conformally flat, we find and our results reduce to earlier ones established by Viaclovsky in 2000 and the second author in 2006.",

keywords = "Conformal transformation, Gauss-Bonnet curvatures, Kazdan-Warner, Locally conformally flat, Renormalized volume coefficients, v curvature, σ curvature",

author = "Bin Guo and Han, {Zheng Chao} and Haizhong Li",

year = "2011",

doi = "10.2140/pjm.2011.251.257",

language = "English (US)",

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pages = "257--268",

journal = "Pacific Journal of Mathematics",

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T1 - Two Kazdan-Warner-type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric

AU - Guo, Bin

AU - Han, Zheng Chao

AU - Li, Haizhong

PY - 2011

Y1 - 2011

N2 - We prove two Kazdan-Warner-type identities involving the renormalized volume coefficients v2k of a Riemannian manifold (Mn, g), the Gauss- Bonnet curvature G2r, and a conformal Killing vector field on (Mn, g). In the case when the Riemannian manifold is locally conformally flat, we find and our results reduce to earlier ones established by Viaclovsky in 2000 and the second author in 2006.

AB - We prove two Kazdan-Warner-type identities involving the renormalized volume coefficients v2k of a Riemannian manifold (Mn, g), the Gauss- Bonnet curvature G2r, and a conformal Killing vector field on (Mn, g). In the case when the Riemannian manifold is locally conformally flat, we find and our results reduce to earlier ones established by Viaclovsky in 2000 and the second author in 2006.

KW - Conformal transformation

KW - Gauss-Bonnet curvatures

KW - Kazdan-Warner

KW - Locally conformally flat

KW - Renormalized volume coefficients

KW - v curvature

KW - σ curvature

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SP - 257

EP - 268

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Two Kazdan-Warner-type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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