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.