N=2 SUPER-WEYL SYMMETRY, SUPER-LIOUVILLE THEORY AND SUPER-RIEMANNIAN SURFACES

The finite form of the N = 2 super-Weyl transformations in the chiral and twisted-chiral irreducible formulations of the two-dimensional N = 2 superfield supergravity are found in N = 2 superspace. The super-Weyl anomaly of the N = 2 extended fermionic string theory is computed in terms of the N = 2 superfields, by using a short-time expansion of the N = 2 chiral heat kernel. The super-Weyl invariant N = 2 superconformal structure is introduced, and a new definition of the N = 2 super-Riemannian surfaces is proposed.