• Journal of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.171-185
• /
• 2009

We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.

• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.384-390
• /
• 2022

In this paper, we study the obstruction on the jets of an almost complex structure J to the existence of a symplectic form ω such that J is compatible with ω. We describe some almost complex structures on ℝ⁴ and on ℝ⁶, respectively, that cannot be calibrated by any symplectic forms. In particular, these examples pertain to the model almost complex structure on ℝ⁴ in [3], and the simple model structure on ℝ⁶ in [7].

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.1069-1091
• /
• 2022

We study almost complex metallic Norden manifolds and their adapted connections with respect to an almost complex metallic Norden structure. We study various connections like special connection of the first type, special connection of the second type, Kobayashi-Nomizu metallic Norden type connection, Yano metallic Norden type connection etc., on almost complex metallic Norden manifolds. We establish classifications of almost complex metallic Norden manifolds by using covariant derivative of the almost complex metallic Norden structure and also by using torsion tensor on the canonical connections.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.4
• /
• pp.417-426
• /
• 2006

In this paper, we are to construct a new fibred Riemannian space with almost complex structure from the lift of an almost contact structures of the base space and that of each fibre. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structure.

• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.379-394
• /
• 2012

Given an almost complex structure ($\mathbb^{C}^m$, J), $m\geq2$, that is defined by setting $\theta^{\alpha}=dz^{\alpha}+a_{\beta}^{\alpha}d\bar{z}^{\beta}$, ${\alpha}=1,\ldots$,m, to be (1, 0)-forms, we find conditions on ($a_{\beta}^{\alpha}$) for the existence of holomorphic functions an classify the almost complex structures by type ($\nu$,q). Then we determine types for several examples in $\mathbb{C}^2$ and $\mathbb{C}^3$ including the natural almost complex structure on $S^6$.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.801-810
• /
• 2022

In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.

• Journal of the Korean Mathematical Society
• /
• v.44 no.1
• /
• pp.237-247
• /
• 2007

In this paper, we establish a necessary condition in terms of curvature for the Kobayashi hyperbolicity of a class of almost complex Finsler manifolds. For an almost complex Finsler manifold with the condition (R), so-called Rizza manifold, we show that there exists a unique connection compatible with the metric and the almost complex structure which has the horizontal torsion in a special form. With this connection, we define a holomorphic sectional curvature. Then we show that this holomorphic sectional curvature of an almost complex submanifold is not greater than that of the ambient manifold. This fact, in turn, implies that a Rizza manifold is hyperbolic if its holomorphic sectional curvature is bounded above by -1.

• Honam Mathematical Journal
• /
• v.43 no.4
• /
• pp.701-715
• /
• 2021

In this paper, we study almost complex Norden Silver manifolds and Kaehler-Norden Silver manifolds. We define adapted connections of first, second and third type to an almost complex Norden Silver manifold and establish the necessary and sufficient conditions for the integrability of almost complex Norden Silver structure. Moreover, we investigate that a complex Norden Silver map is a harmonic map between Kaehler-Norden Silver manifolds.

• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.125-133
• /
• 2011

A new kind of structure is introduced in an even dimensional differentiable Riemannian manifold and some basic properties of this structure is discussed. Also the existence of such structure is shown with an example.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.405-413
• /
• 2005

We consider the connections $\nabla$ on the Rizza manifold (M, J, L) satisfying ${\nabla}G=0\;and\;{\nabla}J=0$. Among them, we derive a Lichnerowicz connection from the Cart an connection and characterize it in terms of torsion. Generalizing Kahler condition in Hermitian geometry, we define a Kahler condition for Rizza manifolds. For such manifolds, we show that the Cartan connection and the Lichnerowicz connection coincide and that the almost complex structure J is integrable.