• 대한수학회지
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• 제21권1호
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• pp.49-61
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• 1984

• 대한수학회논문집
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• 제38권3호
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• pp.865-880
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• 2023

The main intention of the current paper is to characterize certain properties of *-conformal Ricci solitons on non-coKähler (𝜅, 𝜇)-almost coKähler manifolds. At first, we find that there does not exist *-conformal Ricci soliton if the potential vector field is the Reeb vector field θ. We also prove that the non-coKähler (𝜅, 𝜇)-almost coKähler manifolds admit *-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist *-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.507-519
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• 2023

The aim of this paper is to study the Fisher-Marsden conjucture in the frame work of f-cosymplectic and (k, µ)-cosymplectic manifolds. First we prove that a compact f-cosymplectic manifold satisfying the Fisher-Marsden equation R'^*_g = 0 is either Einstein manifold or locally product of Kahler manifold and an interval or unit circle S¹. Further we obtain that in almost (k, µ)-cosymplectic manifold with k < 0, the Fisher-Marsden equation has a trivial solution.

• 대한수학회보
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• 제42권4호
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• pp.817-828
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• 2005

In this note we show that there is an anti-symplectic involution $\sigma\;:\;X\;\to\;X$ on a simply-connected, closed, non-Kahler and symplectic 4-manifold X with a disjoint union of Riemann surfaces ${\amalg}^n_{i=1}{\Sigma}_i,\;n\;{\ge}\;2$ as a fixed point set. Also we show that its quotient X/$\sigma$ is homeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2$ but not diffeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2,\;r\;=\;b_2^-(X/{\sigma})$.

• 대한수학회보
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• 제35권4호
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• pp.669-681
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• 1998

In this paper, we prove that on the complete Kahler manifold, if ${\rho}(x){\geq}-\frac{1}{2}{\lambda}_0$ and either ${\rho}(x_0)>-\frac{1}{2}{lambda}_0$ at some point $x_0$ or Vol(M)=${\infty}$, then the Clifford $L^2$ cohomology group $L^2{\mathcal H}^{\ast}(M,S)$ is trivial, where $\rho(x)$ is the least eigenvalue of ${\mathcal R}_x + \bar{{\mathcal R}}(x)\;and\;{\lambda}_0$ is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M.

• 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.

• 호남수학학술지
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• 제44권3호
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• pp.384-390
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• 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].

• 대한수학회보
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• 제59권4호
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• pp.1011-1018
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• 2022

In this work, magnetic geodesics over the space of Kähler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Ampère equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric Kähler potentials over toric Kähler manifolds.

• 대한수학회지
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• 제61권1호
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• pp.91-107
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• 2024

We determine the N → ∞ asymptotics of the expected value of entanglement entropy for pure states in H_1,N ⊗ H_2,N, where H_1,N and H_2,N are the spaces of holomorphic sections of the N-th tensor powers of hermitian ample line bundles on compact complex manifolds.

• 대한수학회보
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• 제47권1호
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• pp.167-178
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• 2010

We discuss the critical points of the functional $F_{\lambda,\mu}(J,g)=\int_M(\lambda\tau+\mu\tau^*)d\upsilon_g$ on the spaces of all almost Hermitian structures AH(M) with $(\lambda,\mu){\in}R^2-(0,0)$, where $\tau$ and $\tau^*$ being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kahler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals $F_{\lambda,\mu}(J,g)$ on AH(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.