THE GEOMETRY OF COMPLEX CONJUGATE CONNECTIONS

Properties of pairs of conjugate connections are stated with a special view towards the duality of these connections. We express the complex conjugate connections in terms of the structural and the virtual tensors from the almost complex geometry. For a pair of almost complex structures we discuss their mutual recurrence by pointing out that an almost quaternionic structure is implied. The notion of complex conjugate connections is extended in two directions, one called generalized obtained by adding a general (1, 2)-tensor field and the other called exponential since it involves the exponential of the almost complex structure considered.

Keywords:

Almost complex structure, (Conjugate) Linear connection, Hermitian manifold Structural and virtual tensor field, 2000 AMS Classification: 53 B 05,

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