• 제목/요약/키워드: $K{\ddot{a}}hler$

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LOCALLY CONFORMAL KÄHLER MANIFOLDS AND CONFORMAL SCALAR CURVATURE

  • Kim, Jae-Man
    • 대한수학회논문집
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    • 제25권2호
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    • pp.245-249
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    • 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.

ON NEARLY PARAKÄHLER MANIFOLDS

  • Gezer, Aydin;Turanli, Sibel
    • 대한수학회보
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    • 제55권3호
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    • pp.871-879
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    • 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.

ON SOME CLASSES OF ℝ-COMPLEX HERMITIAN FINSLER SPACES

  • Aldea, Nicoleta;Campean, Gabriela
    • 대한수학회지
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    • 제52권3호
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    • pp.587-601
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    • 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.

다양한 탄화수소 연료를 이용한 열방출 섭동 연구 (A Study on Heat Release Fluctuation Using Various Hydrocarbon Fuels)

  • 황동현;안규복
    • 한국추진공학회지
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    • 제20권6호
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    • pp.1-10
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    • 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.

ON VOISIN'S CONJECTURE FOR ZERO-CYCLES ON HYPERKÄHLER VARIETIES

  • Laterveer, Robert
    • 대한수학회지
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    • 제54권6호
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    • pp.1841-1851
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    • 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.

ANTI-SYMPLECTIC INVOLUTIONS ON NON-KÄHLER SYMPLECTIC 4-MANIFOLDS

  • Cho, Yong-Seung;Hong, Yoon-Hi
    • 대한수학회지
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    • 제44권4호
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    • pp.757-766
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    • 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.