Universal deformation rings of string modules over certain class of self-injective special biserial algebras

We determine the universal deformation rings of string Λm.N-modules whose corresponding stable endomorphism ring is isomorphic to k, and which lie either in a connected component of the stable Auslander-Reiten quiver of Λm,N containing a module with endomorphism ring isomorphic to k or in a periodic component containing only string Λm,N-modules, where m≥3 and N≥1 are integers, and Λm,N is a self-injective special biserial k-algebra.