  We adopt a geometric approach to describe the performance of adiabatic
quantum machines, operating under slow time-dependent driving and in contact to
two or more reservoirs with a temperature bias during all the cycle. We show
that the problem of optimizing the power generation of a heat engine and the
efficiency of both the heat engine and refrigerator operational modes is
reduced to an isoperimetric problem with non-trivial underlying metrics and
curvature. This corresponds to the maximization of the ratio between the area
enclosed by a closed curve and its corresponding length. We illustrate this
procedure in a qubit coupled to two reservoirs operating as a thermal machine
by means of an adiabatic protocol.
