Metallic conjugate connections

Abstract

Properties of metallic conjugate connections are stated by pointing out their relation to product conjugate connections. We define the analogous in metallic geometry of the structural and the virtual tensors from the almost product geometry and express the metallic conjugate connections in terms of these tensors. From an applied point of view we consider invariant distributions with respect to the metallic structure and for a natural pair of complementary distributions, the above structural and virtual tensors are expressed in terms of O'Neill–Gray tensor fields.