  A self-consisting gauge-theory approach to describe Dirac fermions on
flexible surfaces with a disclination is formulated. The elastic surfaces are
considered as embeddings into R^3 and a disclination is incorporated through a
topologically nontrivial gauge field of the local SO(3) group which generates
the metric with conical singularity. A smoothing of the conical singularity on
flexible surfaces is naturally accounted for by regarding the upper half of
two-sheet hyperboloid as an elasticity-induced embedding. The availability of
the zero-mode solution to the Dirac equation is analyzed.
