The DoCarmo-Wallach theory studies isometric minimal immersions f: M → Sn of a compact Riemannian homogeneous space M = G/K into Euclidean n-spheres. The parameter space of such immersions is a compact convex body in a representation space for the Lie group G. In this article we give a very general definition of the moduli space and study its geometric properties such as the distortion (as a convex set). In addition, we introduce a general notion of operators, derive various criteria under which they map the moduli into one another, and finally, we show that, under general conditions, the operators are distortion decreasing.
All Science Journal Classification (ASJC) codes
- Moduli spaces
- Spherical maps