Results 11 to 20 of about 14,803 (150)

A note on compact Kähler manifolds with quasi-negative holomorphic sectional curvature

Proceedings of the American Mathematical Society, 2021
A compact Kähler manifold with quasi-negative holomorphic sectional curvature must have ample canonical bundle. This was conjectured by Wu-Yau and is recently proved by the continuity method. In this note, we will give an alternative proof of this result
Wei Xia
semanticscholar   +3 more sources

Quasiprojective manifolds with negative holomorphic sectional curvature [PDF]

Duke Mathematical Journal, 2018
Let $(M,\omega)$ be a compact K\"ahler 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.
Henri Guenancia
semanticscholar   +5 more sources

Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics [PDF]

Science China Mathematics, 2019
We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal Kähler manifold with constant nonpositive holomorphic sectional curvature is Kähler. We also give
Haojie Chen, Lin Chen, Xiaolan Nie
semanticscholar   +5 more sources

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, D. Janssens, F. Tricerri, G. Ganchev, G. Ganchev, Georgi Ganchev, R. Bishop, R. Bryant, S. Kobayashi, S. Tachibana, V. Boju, Vesselka Mihova, Y. Tashiro, Y. Tashiro   +13 more
core   +4 more sources

Hermitian metrics of positive holomorphic sectional curvature on fibrations [PDF]

Mathematische Zeitschrift, 2017
The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration.
Ananya Chaturvedi, Gordon Heier
semanticscholar   +6 more sources

Canonical metric connections with constant holomorphic sectional curvature [PDF]

Pacific Journal of Mathematics
In our previous work, we introduced a special type of Hermitian metrics called {\em torsion-critical,} which are non-K\"ahler critical points of the $L^2$-norm of Chern torsion over the space of all Hermitian metrics with unit volume on a compact complex
Dongmei Zhang, Fangyang Zheng
semanticscholar   +4 more sources

Nonnegative Holomorphic Sectional Curvature on Compact Almost Hermitian Manifolds

Taiwanese Journal of Mathematics
Summary: We study nonnegative holomorphic sectional curvature on a compact almost Hermitian manifold. In the positive case, we show some geometric conditions for negative Kodaira dimension. In the zero case, we give some conditions of the Chern-Yamabe problem for zero Chern scalar curvature.
Masaya Kawamura
semanticscholar   +3 more sources

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.
openaire   +3 more sources

Non-existence of complete Kähler metric of negatively pinched holomorphic sectional curvature [PDF]

Complex Analysis and its Synergies, 2020
We prove a theorem which provides a sufficient condition for the non-existence of a complete Kähler–Einstein metric of negative scalar curvature of which holomorphic sectional curvature is negatively pinched: Let $$\Omega $$ Ω be a bounded weakly ...
Gunhee Cho
semanticscholar   +1 more source

On Bochner Flat Kähler B-Manifolds

Axioms, 2023
We obtain on a Kähler B-manifold (i.e., a Kähler manifold with a Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional
Cornelia-Livia Bejan, Galia Nakova, Adara M. Blaga   +2 more
doaj   +1 more source