• Title/Summary/Keyword: $K{\ddot{a}}hlerian$ manifolds

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LOCALLY SYMMETRIC ALMOST COKÄHLER 5-MANIFOLDS WITH KÄHLERIAN LEAVES

  • Wang, Yaning
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.789-798
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    • 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.

A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄHLER METRICS

  • Kim, Jongsu
    • The Pure and Applied Mathematics
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    • v.20 no.3
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    • pp.199-206
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    • 2013
  • We present a 4-dimensional nil-manifold as the first example of a closed non-K$\ddot{a}$hlerian symplectic manifold with the following property: a function is the scalar curvature of some almost K$\ddot{a}$hler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.

SASAKIAN STRUCTURES ON PRODUCTS OF REAL LINE AND KÄHLERIAN MANIFOLD

  • Beldjilali, Gherici;Cherif, Ahmed Mohammed;Zaga, Kaddour
    • Korean Journal of Mathematics
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    • v.27 no.4
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    • pp.1061-1075
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    • 2019
  • In this paper, we construct a Sasakian manifold by the product of real line and Kählerian manifold with exact Kähler form. This result demonstrates the close relation between Sasakian and Kählerian manifold with exact Kähler form. We present an example and an open problem.