• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.61-66
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• 1984

It is well-known that the most interesting non-integrable almost Hermitian manifold are the nearly Kaehlerian manifolds ([2] and [3]), and that there exists a complex but not a Kaehlerian structure on Riemannian product manifolds of two normal contact manifolds [4]. The purpose of the present paper is to study nearly Kaehlerian product manifolds of two almost contact metric manifolds and investigate the geometrical structures of these manifolds. Unless otherwise stated, we shall always assume that manifolds and quantities are differentiable of class $C^{\infty}$. In Paragraph 1, we give brief discussions of almost contact metric manifolds and their Riemannian product manifolds. In paragraph 2, we investigate the perfect conditions for Riemannian product manifolds of two almost contact metric manifolds to be nearly Kaehlerian and the non-existence of a nearly Kaehlerian product manifold of contact metric manifolds. Paragraph 3 will be devoted to a proof of the following; A conformally flat compact nearly Kaehlerian product manifold of two almost contact metric manifolds is isomatric to a Riemannian product manifold of a complex projective space and a flat Kaehlerian manifold..

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.339-352
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• 1994

A sumbanifold M of a quaternionic Kaehlerian manifold $\tilde{M}^m$ of real dimension 4m is called a generic submanifold if the normal space N(M) of M is always mapped into the tangent space T(M) under the action of the quaternionic Kaehlerian structure tensors of the ambient manifold at the same time.The purpose of the present paper is to study generic submanifold of quaternionic Kaehlerian manifold of constant Q-sectional curvature with nonvanishing parallel mean curvature vector. In section 1, we state general formulas on generic submanifolds of a quaternionic Kaehlerian manifold of constant Q-sectional curvature. Section 2 is devoted to the study generic submanifolds with nonvanishing parallel mean curvature vector and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of those results, in section 3, we prove our main theorems. In this paper, the dimension of a manifold will always indicate its real dimension.

• East Asian mathematical journal
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• v.25 no.4
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• pp.495-504
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• 2009

We introduce three classes of quaternion lightlike submanifolds, screen real lightlike submanifolds and CR lightlike submanifolds of an indefinite quaternion Kaehlerian manifold and study the geometry of leaves of their distributions.

• 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.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.483-500
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• 1997

We investigate the geometric properties reflected by the spectra of the Jacobi operator of a harmonic map when the target manifold is a Riemannian product manifold or a Kaehlerian product manifold. And also we study the spectral characterization of Riemannian sumersions when the target manifold is $S^n \times S^n$ or $CP^n \times CP^n$.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.309-319
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• 1995

Let (M,g) be an m-dimensional compact orientable Riemannian manifold(connected and $C^\infty$) with metric tensor g.

• 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.29 no.1
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• pp.25-29
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• 1992

The purpose of this paper is to study indefinite Kaehlerian metrics with vanishing conformal curvature tensor field. In the first section, a brief summary of the complex version of indefinite Kaehlerian manifolds is recalled and we introduce the conformal curvature tensor field on an indefinite Kaehlerian manifold. In section 2, we obtain the theorem for indefinite Kaehlerian metrics with vanishing conformal curvature tensor field.

• Kyungpook Mathematical Journal
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• v.2 no.2
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• pp.53-60
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• 1959