THE STRUCTURE OF THE REGULAR LEVEL SETS

초록

Consider the L(2)-adjoint s'(g)* of the linearization of the scalar curvature s(g). If ker s'(g)* not equal 0 on an n-dimensional compact manifold, it is well known that the scalar curvature sg is a non-negative constant. In this paper, we study the structure of the level set phi(-1)(0) and find the behavior of Ricci tensor when ker s'(g)* not equal 0 with s(g) > 0. Also for a non-trivial solution (g, f) of z = s'(g)*(f) on an n-dimensional compact manifold, we analyze the structure of the regular level set f(-1)(-1). These results give a good understanding of the given manifolds.

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