Abstract
Much has been studied about an almost complex structure these ten years. One of the problems about the structure is to find an affine connection which makes a given almost complex tensor field parallel. A Riemannian connection is a one without torsion for which the fundamental tensor field of a Riemannian manifold is parallel. Affine connections on the group manifold were investigated fully by E. Cartan in [1]. In this paper we treat in general some tensor fields and affine connections which make the fields parallel. Moreover some studies about certain tensor fields are given.
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