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 twistedchiral 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. Intern. Physics Classification #’s 0465, 1117, 1130 Supported in part by the ’Deutsche Forschungsgemeinschaft’ On leave of absence from: High Current Electronics Institute of the Russian Academy of Sciences, Siberian Branch, Akademichesky 4, Tomsk 634055, Russia Supported in part by the ’Studienstiftung des deutschen Volkes’