The Symplectic Critical Surfaces in a Kähler Surface

2016 ◽  
pp. 185-193 ◽  
Author(s):  
Xiaoli Han ◽  
Jiayu Li ◽  
Jun Sun
Keyword(s):  
Kähler Surface

A Compact Kähler Surface of Negative Curvature Not Covered by the Ball

1980 ◽  
Vol 112 (2) ◽  
pp. 321 ◽  
Author(s):  
G. D. Mostow ◽  
Yum-Tong Siu
Keyword(s):  
Negative Curvature ◽  
Kähler Surface

scholarly journals Special biconformal changes of Kähler surface metrics

2011 ◽  
Vol 167 (3-4) ◽  
pp. 431-448
Author(s):  
Andrzej Derdzinski
Keyword(s):  
Kähler Surface ◽  
Surface Metrics

scholarly journals Twistor Bundle of a Neutral Kähler Surface

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 43
Author(s):  
Włodzimierz Jelonek
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Complex Structure ◽  
Killing Vector ◽  
Kähler Manifold ◽  
Killing Vector Field ◽  
Kahler Manifold ◽  
Kähler Surface ◽  
Kähler Surfaces ◽  
Twistor Bundle

In this paper, we characterize neutral Kähler surfaces in terms of their positive twistor bundle. We prove that an O+,+(2,2)-oriented four-dimensional neutral semi-Riemannian manifold (M,g) admits a complex structure J with ΩJ∈⋀−M, such that (M,g,J) is a neutral-Kähler manifold if and only if the twistor bundle (Z1(M),gc) admits a vertical Killing vector field.

scholarly journals A mean-curvature flow along a Kähler–Ricci flow

2018 ◽  
Vol 29 (01) ◽  
pp. 1850006 ◽  
Author(s):  
Xiaoli Han ◽  
Jiayu Li ◽  
Liang Zhao
Keyword(s):  
Evolution Equation ◽  
Scalar Curvature ◽  
Ricci Flow ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Initial Surface ◽  
Kähler Angle ◽  
Kähler Surface ◽  
The Mean

Let [Formula: see text] be a Kähler surface, and [Formula: see text] an immersed surface in [Formula: see text]. The Kähler angle of [Formula: see text] in [Formula: see text] is introduced by Chern and Wolfson [Am. J. Math. 105 (1983) 59–83]. Let [Formula: see text] evolve along the Kähler–Ricci flow, and [Formula: see text] in [Formula: see text] evolve along the mean-curvature flow. We show that the Kähler angle [Formula: see text] satisfies the evolution equation [Formula: see text] where [Formula: see text] is the scalar curvature of [Formula: see text]. The equation implies that if the initial surface is symplectic (Lagrangian), then, along the flow, [Formula: see text] is always symplectic (Lagrangian) at each time [Formula: see text], which we call a symplectic (Lagrangian) Kähler–Ricci mean-curvature flow. In this paper, we mainly study the symplectic Kähler–Ricci mean-curvature flow.

scholarly journals EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES

2020 ◽  
Vol 8 ◽  
Author(s):  
JIYUAN HAN ◽  
JEFF A. VIACLOVSKY
Keyword(s):  
Compact Subset ◽  
Moduli Spaces ◽  
Convergent Subsequence ◽  
Kähler Metrics ◽  
Compactness Result ◽  
Kahler Metrics ◽  
Asymptotically Locally Euclidean ◽  
Kähler Surface ◽  
Kähler Surfaces

Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kähler metrics on a minimal Kähler surface whose Kähler classes stay in a compact subset of the interior of the Kähler cone must have a convergent subsequence. As an application, we prove the existence of global moduli spaces of scalar-flat Kähler ALE metrics for several infinite families of Kähler ALE spaces.

The Donaldson-Hitchin-Kobayashi Correspondence for Parabolic Bundles over Orbifold Surfaces

2001 ◽  
Vol 53 (6) ◽  
pp. 1309-1339 ◽  
Author(s):  
Brian Steer ◽  
Andrew Wren
Keyword(s):  
Riemann Surfaces ◽  
Einstein Metrics ◽  
Approximation Theorem ◽  
Effective Divisor ◽  
Parabolic Bundles ◽  
Kähler Surface ◽  
Holomorphic Bundles ◽  
Suitable Approximation

AbstractA theorem of Donaldson on the existence of Hermitian-Einstein metrics on stable holomorphic bundles over a compact Kähler surface is extended to bundles which are parabolic along an effective divisor with normal crossings. Orbifold methods, together with a suitable approximation theorem, are used following an approach successful for the case of Riemann surfaces.

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