Local isometric imbedding of a compact Riemann surface with a singular non-CSC extremal Kähler metric into 3-dimension space forms

DOI10.1007/S12220-021-00756-4zbMath1487.53027OpenAlexW4200562843WikidataQ114221031 ScholiaQ114221031MaRDI QIDQ2061542

Zhiqiang Wei, Yingyi Wu

Publication date: 15 December 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-021-00756-4

zbMATH Keywords

umbilicalextremal Kähler metricHessian of the curvatureMoving frames

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Exterior differential systems (Cartan theory) (58A15) Local submanifolds (53B25)

Related Items (1)

On minimal immersions of a singular non-CSC extremal Kähler metric into 3-dimensional space forms

Cites Work

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• Character 1-form and the existence of an HCMU metric
• On one-dimensional and singular Calabi's extremal metrics whose Gauss curvatures have nonzero umbilical Hessians
• Existence and explicit constructions of HCMU metrics on \(\text{S}^{2}\) and \(\text{T}^{2}\)
• Extremal Hermitian metrics on Riemann surfaces
• Weak limits of Riemannian metrics in surfaces with integral curvature bound
• Obstruction to the existence of metric whose curvature has umbilical Hessian in a \(K\)-surface
• Extremal Hermitian metrics on Riemann surfaces with singularities
• Explicit construction of extremal Hermitian metrics with finite conical singularities on \(S^2\)
• One existence theorem for non-CSC extremal Kähler metrics with conical singularities on \(S^2\)
• A one-dimensional singular non-CSC extremal Kähler metric can be isometrically imbedded into \(\mathbb{R}^3\) as a Weingarten surface
• Submanifold theory. Beyond an introduction
• On the existence of non-CSC extremal Kähler metrics with finite singularities on \(S^2\)
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Seminar on Differential Geometry. (AM-102)
• Calabi's conjecture and some new results in algebraic geometry
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

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