Abstract
In this paper,we study the thermodynamic properties of a toroidal black hole from a geometric viewpoint.After the temperature and heat capacity of the black hole have been calculated,we investigate the relationship between its thermodynamic geometry metric and critical behavior,as well as phase transition characteristics.The results show that the temperature of the toroidal black hole is equal to its Hawking temperature.Moreover,because its curvature scalar is zero,the Weinhold geometry fails to provide some information about the critical behavior and phase transition characteristics of the toroidal black hole.But the Ruppeiner geometry and the Legendre invariant metric can provide a good description of its phase structure.
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