Because of their nice topological properties K/hler mnifolds hve been studied much more extensively than other kinds of almost Hermitian mani- folds. In the study of non-K/hler almost Hermitian manifolds it is natural to consider those whose almost complex structure satisfies similar but weaker conditions than those of Kahler manifolds. Calabi and Eckmann [3] have
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Alfred Gray (1966) studied this question.