• Bulletin of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.137-145
• /
• 2004

In [13], we developed a theory of complex Finsler manifolds to investigate the global geometry of complex Finsler manifolds. There we proved a version of Bonnet-Myers' theorem for complex Finsler manifolds with a certain condition on the Finsler metric which is a generalization of the Kahler condition for the Hermitian metric. In this paper, we show that if the holomorphic sectional curvature of M is ${\geq}\;c^2\;>\;0$, then M is simply connected. This is a generalization of the Synge's theorem in the Riemannian geometry and the Tsukamoto's theorem for Kahler manifolds. The main point of the proof lies in how we can circumvent the convex neighborhood theorem in the Riemannian geometry. A second variation formula of arc length for complex Finsler manifolds is also derived.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.83-90
• /
• 2016

We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.

• Communications of the Korean Mathematical Society
• /
• v.29 no.4
• /
• pp.569-579
• /
• 2014

We consider a condition under which the projectivization $P(E^k)$ of a complex k-bundle $E^k{\rightarrow}M$ over an even-dimensional manifold M can have the hard Lefschetz property, affected by [10]. It depends strongly on the rank k of the bundle $E^k$. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.

• Communications of the Korean Mathematical Society
• /
• v.18 no.2
• /
• pp.309-323
• /
• 2003

In this paper, We characterize a semi-invariant sub-manifold of codimension 3 satisfying ∇$\varepsilon$A = 0 in a complex projective space CP$\^$n+1/, where ∇$\varepsilon$A is the covariant derivative of the shape operator A in the direction of the distinguished normal with respect to the structure vector field $\varepsilon$.

• The Pure and Applied Mathematics
• /
• v.17 no.1
• /
• pp.51-63
• /
• 2010

In this paper, we prove two characterization theorems for real half lightlike submanifold (M,g,S(TM)) of an indefinite Kaehler manifold $\bar{M}$ or an indefinite complex space form $\bar{M}$(c) subject to the conditions : (a) M is totally umbilical in $\bar{M}$, or (b) its screen distribution S(TM) is totally umbilical in M.

• 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.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.747-756
• /
• 2003

We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.

• Communications of the Korean Mathematical Society
• /
• v.14 no.1
• /
• pp.201-210
• /
• 1999

We introduce the notion of the Finsler metrics compatible with f(5,1)-structure and investigate the properties of Finsler space with such metrics.

• Journal of the Korean Mathematical Society
• /
• v.43 no.6
• /
• pp.1289-1300
• /
• 2006

It is well known that the twistor, section of twistor space, classify the orthogonal almost complex structure on even dimensional Riemannian manifold (X, g). We will show that existence of a harmonic and anti-holomorphic twistor is equivalent to having a symplectic structure on (X, g).

• East Asian mathematical journal
• /
• v.15 no.1
• /
• pp.147-151
• /
• 1999