  Following P. M. H. Wilson's paper on sectional curvatures of Kahler moduli,
we consider a natural Riemannian metric on a hypersurface f=1 in a real vector
space, defined using the Hessian of a homogeneous polynomial f. We give
examples to answer a question by Wilson about when this metric has nonpositive
curvature.
  Also, we exhibit a large class of polynomials f on R^3 such that the
associated metric has constant negative curvature. Dubrovin found another such
polynomial on R^3, the Maschke sextic. We ask if these examples are the only
ones with constant negative curvature, and we prove some partial results. This
question is related both to the WDVV equations from string theory and to the
"Clebsch covariant" from 19th-century invariant theory.
