SCALAR CURVATURE AND CONFORMAL DEFORMATION OF HYPERBOLIC SPACE

Let (H(m), g(H)), m greater-than-or-equal-to 3, be the m-dimensional hyperbolic space with its Riemannian metric g(H), of sectional curvature - 1; and let K be a smooth function on H(m). In the first part of this article we establish sufficient conditions for K to be-respectively, not to be-the scalar curvature of some complete metric u4/(m-2)g(H) pointwise conformal to g(H). In the second part we prove results for the two-dimensional case, singularity and uniquens questions. (C) 1994 Academic Press, Inc.