• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.649-658
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• 1994

The notion of the almost Hermitian Finsler manifold admitting an almost complex structure $f^i_j(x)$ was, for the first time, introduced by G. B. Rizza [8]. It is known that the almost Hermitian Finsler manifold (or a Rizza manifold) has been studied by Y. Ichijyo [2] and H. Hukui [1]. In those papers, the almost Hermitian Finsler manifold which the h-covariant derivative of the almost complex structure $f^i_j(x)$ with respect to the Cartan's Finsler connection vanishes was defined as the Kaehlerian Finsler manifold. The nearly Kaehlerian Finsler manifold was defined and studied by the former of authors [7]. The present paper is the continued study of above paper.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.505-517
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• 2002

We introduce certain conformally invariant h-Finsler connection in a Rizza manifold. Using this connection, we find some conformally invariant Finsler tensors. The conformal flatness and the Kaehlerian Finsler manifold with respect to the above connection are investigated.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.375-384
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• 1995

The almost Hermitian Finsler structure of a Rizza manifold is an almost Hermitian structure if a special condition satisfies. In this paper, the induced Finsler connection from Moor metric is define and the some properties of a Kaehlerian Finsler manifold with respect to the induced Finsler connection from Moor metric are investigated.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.327-340
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• 2003

We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

• East Asian mathematical journal
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• v.11 no.2
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• pp.315-319
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• 1995