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On nearly Kähler Finsler spaces. (English) Zbl 1431.53026

Summary: Ichijyō introduced \((a, b, J)\)-manifolds as a special class of generalized Randers manifolds. We introduce generalized \((a, b, J)\)-manifolds. A partial negative answer to Ichijyō’s open problem on nearly Kähler Finsler manifolds is given. The condition under which generalized \((a, b, J)\)-manifolds are Berwaldian is obtained. Finally, we prove that under a mild assumption a nearly Kähler Finsler manifold is Landsbergian.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53B35 Local differential geometry of Hermitian and Kählerian structures
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