• Title/Summary/Keyword: hyperbolic 3-manifold

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ON THE VOLUMES OF CANONICAL CUSPS OF COMPLEX HYPERBOLIC MANIFOLDS

  • Kim, In-Kang;Kim, Joon-Hyung
    • Journal of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.513-521
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    • 2009
  • We first introduce a complex hyperbolic space and a complex hyperbolic manifold. After defining the canonical horoball and the canonical cusp on the complex hyperbolic manifold, we estimate the volumes of canonical cusps of complex hyperbolic manifolds. Finally, we deal with cusped, complex hyperbolic 2-manifolds, and in particular, the ones with only one cusp.

GENERALIZED m-QUASI-EINSTEIN STRUCTURE IN ALMOST KENMOTSU MANIFOLDS

  • Mohan Khatri;Jay Prakash Singh
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.717-732
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    • 2023
  • The goal of this paper is to analyze the generalized m-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized m-quasi-Einstein structure (g, f, m, λ) is locally isometric to a hyperbolic space ℍ2n+1(-1) or a warped product ${\tilde{M}}{\times}{_{\gamma}{\mathbb{R}}$ under certain conditions. Next, we proved that a (κ, µ)'-almost Kenmotsu manifold with h' ≠ 0 admitting a closed generalized m-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized m-quasi-Einstein metric (g, f, m, λ) in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(-4) × ℝ.

SOME HYPERBOLIC SPACE FORMS WITH FEW GENERATED FUNDAMENTAL GROUPS

  • Cavicchioli, Alberto;Molnar, Emil;Telloni, Agnese I.
    • Journal of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.425-444
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    • 2013
  • We construct some hyperbolic hyperelliptic space forms whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane re ections and half-turns. Then we describe covering properties and determine the isometry groups of the constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp.

SOME EXAMPLES OF HYPERBOLIC HYPERSURFACES IN THE COMPLEX PROJECTIVE SPACE

  • Fujimoto, Hirotaka
    • Journal of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.595-607
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    • 2003
  • In the previous paper [6], the author constructed hyperbolic hypersurfaces of degree $2^{n}$ in the n-dimensional complex projective space for every $n\;\geq\;3$. The purpose of this paper is to give some improvement of this result and to show some general methods of constructions of hyperbolic hypersurfaces of higher degree, which enable us to construct hyperbolic hypersurfaces of degree d in the n-dimensional complex projective space for every $d\;\geq\;2\;{\times}\;6^{n}$.

FACE PAIRING MAPS OF FORD DOMAINS FOR CUSPED HYPERBOLIC 3-MANIFOLDS

  • Hong, Sung-Bok;Kim, Jung-Soo
    • Journal of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.1007-1025
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    • 2008
  • We will describe a way to construct Ford domains of cusped hyperbolic 3-manifolds on maximal cusp diagrams and compute fundamental groups using face pairing maps as generators and Cannon-Floyd-Parry's edge cycles as relations. We also describe explicitly a cutting and pasting alteration to reduce the number of faces on the bottom region of Ford domains. We expect that our analysis of Ford domains will be useful on other future research.

KENMOTSU MANIFOLDS SATISFYING THE FISCHER-MARSDEN EQUATION

  • Chaubey, Sudhakar Kr;De, Uday Chand;Suh, Young Jin
    • Journal of the Korean Mathematical Society
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    • v.58 no.3
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    • pp.597-607
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    • 2021
  • The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies 𝔏*g(λ) = 0 on a (2n + 1)-dimensional Kenmotsu manifold M2n+1, then either ξλ = -λ or M2n+1 is Einstein. If n = 1, M3 is locally isometric to the hyperbolic space H3 (-1).