• 대한수학회논문집
• /
• 제25권2호
• /
• pp.245-249
• /
• 2010

We show that on a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ (dim $M^{2n}\;=\;2n\;{\geq}\;4$), $M^{2n}$ is K$\ddot{a}$hler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of $M^{2n}$ everywhere. As a consequence, if a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ is both conformally flat and scalar flat, then $M^{2n}$ is K$\ddot{a}$hler. In contrast with the compact case, we show that there exists a locally conformal K$\ddot{a}$hler manifold with k equal to s, which is not K$\ddot{a}$hler.

• 대한수학회논문집
• /
• 제27권1호
• /
• pp.197-200
• /
• 2012

Concerning the integrability of almost K$\ddot{a}$hler manifolds, we prove that a compact almost K$\ddot{a}$hler locally symmetric space is K$\ddot{a}$hler if the length of the star Ricci tensor is not smaller than that of the Ricci tensor.

• 대한수학회보
• /
• 제55권3호
• /
• pp.871-879
• /
• 2018

The purpose of the present paper is to study on nearly $paraK{\ddot{a}}hler$ manifolds. Firstly, to investigate some properties of the Ricci tensor and the $Ricci^*$ tensor of nearly $paraK{\ddot{a}}hler$ manifolds. Secondly, to define a special metric connection with torsion on nearly $paraK{\ddot{a}}hler$ manifolds and present its some properties.

• 대한수학회보
• /
• 제56권1호
• /
• pp.219-228
• /
• 2019

In this paper it is proved that on an almost $coK{\ddot{a}}hler$ 3-manifold M, (i) M is h-semisymmetric, (ii) the curvature condition $Q{\cdot}R=0$ and (iii) M is $coK{\ddot{a}}hler$ are equivalent.

• 대한수학회지
• /
• 제52권3호
• /
• pp.587-601
• /
• 2015

In this paper, we investigate the $\mathbb{R}$-complex Hermitian Finsler spaces, emphasizing the differences that separate them from the complex Finsler spaces. The tools used in this study are the Chern-Finsler and Berwald connections. By means of these connections, some classes of the $\mathbb{R}$-complex Hermitian Finsler spaces are defined, (e.g. weakly K$\ddot{a}$hler, K$\ddot{a}$hler, strongly K$\ddot{a}$hler). Here the notions of K$\ddot{a}$hler and strongly K$\ddot{a}$hler do not coincide, unlike the complex Finsler case. Also, some kinds of Berwald notions for such spaces are introduced. A special approach is devoted to obtain the equivalence conditions for an $\mathbb{R}$-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an $\mathbb{R}$-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.767-781
• /
• 1996

We shall prove some vanishing theorems for the tranversal Dirac operators on $K\ddot{a}$hler foliations.

• 대한수학회보
• /
• 제55권3호
• /
• pp.789-798
• /
• 2018

Let M be a compact almost $coK{\ddot{a}}hler$ 5-manifold with $K{\ddot{a}}hlerian$ leaves. In this paper, we prove that M is locally symmetric if and only if it is locally isometric to a Riemannian product of a unit circle $S^1$ and a locally symmetric compact $K{\ddot{a}}hler$ 4-manifold.

• 한국추진공학회지
• /
• 제20권6호
• /
• pp.1-10
• /
• 2016

연소불안정 능동제어를 위해서는 음향 발생기나 2차 연료 분사를 통해 압력 섭동이나 열방출 섭동에 변화를 주어야 한다. 2차 연료 분사의 위치 및 시점을 결정하기 위해서는 연소불안정 시 발생하는 열방출 섭동의 분포를 알아야 한다. 본 연구에서는 탄화수소 연료, 유입 속도, 당량비, 음향가진 조건을 변화시키며 위상에 따른 열방출 섭동의 분포를 실험적으로 측정하였다. 와류 발생에 따른 열방출 섭동은 $Damk{\ddot{o}}hler$ 수에 의해 크게 영향을 받는 것을 알 수 있었다. $Damk{\ddot{o}}hler$ 수가 대략 4 - 5 보다 큰 경우는 와류의 leading edge에서 hot spot이 trailing edge에서 cold spot이 발생하였다. 이와는 반대로 $Damk{\ddot{o}}hler$ 수가 3 보다 작은 경우는 반대의 경향이 나타남을 확인할 수 있었다.

• 대한수학회지
• /
• 제54권6호
• /
• pp.1841-1851
• /
• 2017

Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin's conjecture in the setting of $hyperk{\ddot{a}}hler$ varieties, and we prove this reformulated conjecture for one family of $hyperk{\ddot{a}}hler$ fourfolds.

• 대한수학회지
• /
• 제44권4호
• /
• pp.757-766
• /
• 2007

In this note we construct an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold which is constructed by Thurston and show that the quotient of the Thurston's 4-manifold is not symplectic. Also we construct a non-$K\ddot{a}hler$, symplectic 4-manifold using the Gomph's symplectic sum method and an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold.