Obstruction to the existence of metric whose curvature has umbilical Hessian in a \(K\)-surface

DOI10.4310/CAG.2000.V8.N2.A2zbMath0971.53029MaRDI QIDQ1576540

Xiuxiong Chen

Publication date: 21 October 2001

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

zbMATH Keywords

scalar curvatureHessianKilling vector fieldoptimal metric\(K\)-surface

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Critical metrics (58E11)

Related Items (14)

HCMU surfaces and Weingarten surfaces ⋮ Multi-valued holomorphic functions and non-CSC extremal Kähler metrics with singularities on compact Riemann surfaces ⋮ On the existence of non-CSC extremal Kähler metrics with finite singularities on \(S^2\) ⋮ On one-dimensional and singular Calabi's extremal metrics whose Gauss curvatures have nonzero umbilical Hessians ⋮ A one-dimensional singular non-CSC extremal Kähler metric can be isometrically imbedded into \(\mathbb{R}^3\) as a Weingarten surface ⋮ Character 1-form and the existence of an HCMU metric ⋮ Non-CSC extremal Kähler metrics on \(S^2_{\{2,2,2\}}\) ⋮ One existence theorem for non-CSC extremal Kähler metrics with conical singularities on \(S^2\) ⋮ New proof of a Calabi's theorem ⋮ Spectral properties of reducible conical metrics ⋮ Rigidity of a family of spherical conical metrics ⋮ Local isometric imbedding of a compact Riemann surface with a singular non-CSC extremal Kähler metric into 3-dimension space forms ⋮ Explicit isometric immersions from footballs to \(\mathbb{R}^3\) ⋮ On minimal immersions of a singular non-CSC extremal Kähler metric into 3-dimensional space forms

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