• Title/Summary/Keyword: Kahler manifold

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MIAO-TAM EQUATION ON ALMOST COKÄHLER MANIFOLDS

  • Mandal, Tarak
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.881-891
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    • 2022
  • In the present paper, we have studied Miao-Tam equation on three dimensional almost coKähler manifolds. We have also proved that there does not exist non-trivial solution of Miao-Tam equation on the said manifolds if the dimension is greater than three. Also we give an example to verify the deduced results.

KÄHLER SUBMANIFOLDS WITH LOWER BOUNDED TOTALLY REAL BISECTIONL CURVATURE TENSOR II

  • Pyo, Yong-Soo;Shin, Kyoung-Hwa
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.279-293
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    • 2002
  • In this paper, we prove that if every totally real bisectional curvature of an n($\geq$3)-dimensional complete Kahler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than (equation omitted) (3n$^2$+2n-2), then it is totally geodesic and compact.

A NOTE ON INDECOMPOSABLE 4-MANIFOLDS

  • Cho, Yong-Seung;Hong, Yoon-Hi
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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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 $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2,\;r\;=\;b_2^-(X/{\sigma})$.

CLAIRAUT POINTWISE SLANT RIEMANNIAN SUBMERSION FROM NEARLY KÄHLER MANIFOLDS

  • Gauree Shanker;Ankit Yadav
    • Honam Mathematical Journal
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    • v.45 no.1
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    • pp.109-122
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    • 2023
  • In the present article, we introduce pointwise slant Riemannian submersion from nearly Kähler manifold to Riemannian manifold. We established the conditions for fibers to be totally geodesic. We also find necessary and sufficient conditions for pointwise slant submersion 𝜑 to be a harmonic and totally geodesic. Further, we study clairaut pointwise slant Riemannian submersion from nearly Kähler manifold to Riemannian manifold. We derive the clairaut conditions for 𝜑 such that 𝜑 is a clairaut map. Finally, one example is constructed which demonstrates existence of clairaut pointwise slant submersion from nearly Kähler manifold to Riemannian manifold.

RELATIVE TWISTED KÄHLER-RICCI FLOWS ON FAMILIES OF COMPACT KÄHLER MANIFOLDS

  • Choi, Young-Jun
    • East Asian mathematical journal
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    • v.37 no.5
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    • pp.577-584
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    • 2021
  • Let p : X → D be a proper surjective holomorphic submersion where X is a Kähler manifold and D is the unit disc in ℂ. Let Ω be a d-closed semi-positive real (1, 1)-form on X. If each Xs := p-1(s) for s ∈ D satisfies $-c_1(X_s)+{\Omega}{\mid}_{X_s}$ is Kähler, then the Kähler-Ricci flow twisted by ${\Omega}{\mid}_{X_s}$ has a long time solution by Cao's theorem. This family of twisted Kähler-Ricci flows induces a relative Kähler form ω(t) on the total space X. In this paper, we prove that the positivity of ω(t) is preserved along the twisted Kähler-Ricci flow.

A NEW TYPE WARPED PRODUCT METRIC IN CONTACT GEOMETRY

  • Mollaogullari, Ahmet;Camci, Cetin
    • Honam Mathematical Journal
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    • v.44 no.1
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    • pp.62-77
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    • 2022
  • This study presents an 𝛼-Sasakian structure on the product manifold M1 × 𝛽(I), where M1 is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

ON THE SYNGE'S THEOREM FOR COMPLEX FINSLER MANIFOLDS

  • Won, Dae-Yeon
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.1
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    • pp.137-145
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    • 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.

CLIFFORD $L^2$-COHOMOLOGY ON THE COMPLETE KAHLER MANIFOLDS II

  • Bang, Eun-Sook;Jung, Seoung-Dal;Pak, Jin-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.4
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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.

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ON REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM (II)

  • Pyo, Yong-Soo
    • Communications of the Korean Mathematical Society
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    • v.9 no.2
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    • pp.369-383
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    • 1994
  • A complex n-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_{n}$ (c). A complete and simply connected complex space form consists of a complex projective space $P_{n}$ C, a complex Euclidean space $C^{n}$ or a complex hyperbolic space $H_{n}$ C, according as c > 0, c = 0 or c < 0.(omitted)

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AVERAGE ENTROPY AND ASYMPTOTICS

  • Tatyana Barron;Manimugdha Saikia
    • Journal of the Korean Mathematical Society
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    • v.61 no.1
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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 H1,N ⊗ H2,N, where H1,N and H2,N are the spaces of holomorphic sections of the N-th tensor powers of hermitian ample line bundles on compact complex manifolds.