Results 11 to 20 of about 4,520 (139)
Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature
Acta Mathematica Sinica, English Series, 2022 A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler when the constant is non-zero and must be Chern flat when the constant is zero. The conjecture is known in complex dimension $2$ by the work of Balas-Gauduchon in 1985 (when the constant is zero or negative)
Rao, Pei Pei, Zheng, Fang Yang
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Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics [PDF]
Science China Mathematics, 2019 19 ...
Chen, Haojie +2 more
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Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures [PDF]
Open Mathematics, 2005 The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric ...
A. Gray +13 more
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Hermitian metrics of positive holomorphic sectional curvature on fibrations [PDF]
Mathematische Zeitschrift, 2019 This is a pre-print of an article published in Mathematische Zeitschrift.
Chaturvedi, Ananya, Heier, Gordon
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Holomorphic sectional curvature, nefness and Miyaoka–Yau type inequality [PDF]
Mathematische Zeitschrift, 2020 On a compact K hler manifold, we introduce a notion of almost nonpositivity for the holomorphic sectional curvature, which by definition is weaker than the existence of a K hler metric with semi-negative holomorphic sectional curvature. We prove that a compact K hler manifold of almost nonpositive holomorphic sectional curvature has a nef canonical ...
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Symplectic mean curvature flows in Kähler surfaces with positive holomorphic sectional curvatures [PDF]
Geometriae Dedicata, 2013 In this paper, we mainly study the mean curvature flow in K hler surfaces with positive holomorphic sectional curvatures. We prove that if the ratio of the maximum and the minimum of the holomorphic sectional curvatures is less than 2, then there exists a positive constant $ $ depending on the ratio such that $\cos \geq $ is preserved along the ...
Jiayu Li, Liuqing Yang
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Compact Hermitian manifolds of constant holomorphic sectional curvature
Mathematische Zeitschrift, 1985 Although compact Kähler manifolds of constant holomorphic sectional curvature have been classified [\textit{S. Kobayashi} and \textit{K. Nomizu}, Foundations of differential geometry, vol. II (1969; Zbl 0175.485)], little is known of the more general Hermitian case.
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Quasiprojective manifolds with negative holomorphic sectional curvature [PDF]
Duke Mathematical Journal, 2022 Let $(M, )$ be a compact K hler manifold with negative holomorphic sectional curvature. It was proved by Wu-Yau and Tosatti-Yang that $M$ is necessarily projective and has ample canonical bundle. In this paper, we show that any irreducible subvariety of $M$ is of general type.
Zhang, Yashan, Zheng, Tao
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Complex nilmanifolds with constant holomorphic sectional curvature [PDF]
Proceedings of the American Mathematical Society, 2021 A well known conjecture in complex geometry states that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler if the constant is non-zero and must be Chern flat if the constant is zero. The conjecture is confirmed in complex dimension $2$, by the work of Balas-Gauduchon in 1985 (when the constant is zero or negative)
Li, Yulu, Zheng, Fangyang
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Spaces of constant para-holomorphic sectional curvature [PDF]
Pacific Journal of Mathematics, 1989 A \((J^ 4=1)\)-structure on an \(n\)-dimensional manifold \(M\) is a tensor field of type \((1,1)\) on \(M\) such that \(J^ 4=1\). Its characteristic polynomial is \((x-1)^{r_ 1}(x+1)^{r_ 2}(x^ 2+1)^ s\), where \(r_ 1+r_ 2+s=n\). In particular, one obtains the almost complex structure, the almost product structure and the almost hyperbolic complex ...
Gadea, P. M., Montesinos Amilibia, A.
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