THE STRUCTURE OF THE REGULAR LEVEL SETS

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

Abstract
Consider the $\small{L^2}$-adjoint $\small{s_g^{$ of the linearization of the scalar curvature $\small{s_g}$. If ker $\small{s_g^{$ on an n-dimensional compact manifold, it is well known that the scalar curvature $\small{s_g}$ is a non-negative constant. In this paper, we study the structure of the level set $\small{{\varphi}^{-1}}$(0) and find the behavior of Ricci tensor when ker $\small{s_g^{$ with $\small{s_g}$ > 0. Also for a nontrivial solution (g, f) of $\small{z=s_g^{$ on an n-dimensional compact manifold, we analyze the structure of the regular level set $\small{f^{-1}}$(-1). These results give a good understanding of the given manifolds.
Keywords
scalar curvature;the regular level set;the traceless Ricci tensor;
Language
English
Cited by
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