THE STRUCTURE OF THE REGULAR LEVEL SETS

Hwang, Seung-Su

doi:10.4134/BKMS.2011.48.6.1245

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THE STRUCTURE OF THE REGULAR LEVEL SETS

Journal title : Bulletin of the Korean Mathematical Society
Volume 48, Issue 6, 2011, pp.1245-1252
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2011.48.6.1245

Title & Authors

THE STRUCTURE OF THE REGULAR LEVEL SETS
Hwang, Seung-Su;

Abstract

Consider the ${$L^2$}$ -adjoint ${$s_g^{`*}$}$ of the linearization of the scalar curvature ${$s_g$}$ . If ker ${$s_g^{`*}{\neq}0$}$ on an n-dimensional compact manifold, it is well known that the scalar curvature ${$s_g$}$ is a non-negative constant. In this paper, we study the structure of the level set ${${\varphi}^{-1}$}$ (0) and find the behavior of Ricci tensor when ker ${$s_g^{`*}{\neq}0$}$ with ${$s_g$}$ > 0. Also for a nontrivial solution (g, f) of $z

Keywords

scalar curvature;the regular level set;the traceless Ricci tensor;

Language

English

Cited by

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