Abstract
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.
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