Nonlinear models in 2+epsilon dimensions

A generalization of the nonlinear sigma model is considered. The field takes values in a compact manifold M and the coupling is determined by a Riemannian metric on M. The model is renormalizable in 2+epsilon dimensions, the renormalization group acting on the infinite-dimensional space of Riemannian metrics. Topological properties of the β function and solutions of the fixed-point equation R/sub i/j-αg/sub i/j=del/sub i/v/sub j/+ del/sub j/v/sub i/, α= +- 1 or 0, are discussed