  Thermodynamic properties of locally anisotropic (2+1)-black holes are studied
by applying geometric methods. We consider a new class of black holes with a
constant in time elliptical event horizon which is imbedded in a generalized
Finsler like spacetime geometry induced from Einstein gravity. The
corresponding thermodymanic systems are three dimensional with entropy S being
a hypersurface function on mass M, anisotropy angle $\theta$ and eccentricity
of elliptic deformations $\epsilon$. Two-dimensional curved thermodynamic
geometries for locally anistropic deformed black holes are constructed after
integration on anisotropic parameter $\theta$. Two approaches, the first one
based on two-dimensional hypersurface parametric geometry and the second one
developed in a Ruppeiner-Mrugala-Janyszek fashion, are analyzed. The
thermodynamic curvatures are computed and the critical points of curvature
vanishing are defined.
