An absolute parallelism (AP-) space having Finslerian properties is called FAP-space. This FAP-structure is wider than both conventional AP and Finslerstructures. In the present work, more geometric objects as curvature and torsiontensors are derived in the context of this structure. Also second order tensors,usually needed for physical applications, are derived and studied. Furthermore,the anti-curvature and the W-tensor are defned for the FAP-structure. Relationsbetween Riemannian, AP, Finsler and FAP structures are given.
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