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In this work we provide a possible geometrical interpretation of the spin ofelementary particles. In particular, it is investigated how the wave equationsof matter are altered by the addition of an antisymmetric contribution to themetric tensor. In this scenario the explicit form of the matter wave equationsis investigated in a general curved space-time, and then the equations areparticularized to the flat case. Unlike traditional approaches of NGT, in whichthe gravitational field is responsible for breaking the symmetry of the flatMinkowski metric, we find more natural to consider that, in general, the metricof the space-time could be nonsymmetric even in the flat case. The physicalconsequences of this assumption are explored in detail. Interestingly enough,it is found that the metric tensor splits into a bosonic and a fermionic; theantisymmetric part of the metric is very sensitive to the spin and turns out tobe undetectable for spinless scalar particles. However, fermions couple to itin a non-trivial way (only when there are interactions). In addition, the Paulicoupling is derived automatically as a consequence of the nonsymmetric natureof the metric

Implications of nonsymmetric metric theories for particle physics. New interpretation of the Pauli coupling