Abstract: Abstract. The Chern connection was defined in 1946 in the almost Hermitian geometry, and in 2005 in the almost paraHermitian context. In 2017, it was proved that the condition defining the Chern connection does not determine a unique connection in the other two (J2 = ±1)- metric geometries (almost Norden and almost product Riemannian with null trace). Now, we prove that there exists a unique canonical connection satisfying the Chern condition in these two geometries if and only if the manifold is of type G1. For such a characterization, we need an exhaustive study of the plane of quasi-canonical connections, defined by the Levi-Civita connection and the line of canonical connections. Connections with totally skew-symmetric torsion also have an important role.

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