A new variational characterization of 𝑛-dimensional space forms

DOI10.1090/S0002-9947-03-03486-XzbMath1058.53029OpenAlexW1944011715MaRDI QIDQ4813795

Haizhong Li, Ze-Jun Hu

Publication date: 13 August 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03486-x

zbMATH Keywords

functionalsconformally flatRiemannian metricsSchouten tensorelementary symmetric function of the eigenvalues

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20)

Related Items (19)

A note on a formal Riemannian structure on conformal classes ⋮ Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds ⋮ On the variation of a metric and its application ⋮ Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds ⋮ The \(k\)-Yamabe solitons and the quotient Yamabe solitons ⋮ Some rigidity results on critical metrics for quadratic functionals ⋮ Variational formulae of some functionals by the modified Schouten tensor ⋮ The stability of Fubini-Study metric on $\mathbb {CP}^n$ ⋮ Some characterizations on critical metrics for quadratic curvature functions ⋮ On the \(\sigma_2\)-curvature and volume of compact manifolds ⋮ Critical metrics of the Schouten functional ⋮ Two rigidity theorems for fully nonlinear equations ⋮ Projective Blaschke manifolds ⋮ Bach-flat critical metrics for quadratic curvature functionals ⋮ On variational formulas of a conformally invariant functional ⋮ Some rigidity characterizations on critical metrics for quadratic curvature functionals ⋮ Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals ⋮ Some rigidity properties for manifolds with constant \(k\)-curvature of modified Schouten tensor ⋮ Unnamed Item

Cites Work

• Einige differentialgeometrische Kongruenzsätze für geschlossene Flächen und Hyperflächen
• Propagateurs et commutateurs en relativité générale
• Global rigidity theorems of hypersurfaces
• Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• Conformal geometry, contact geometry, and the calculus of variations
• The splitting theorem for manifolds of nonnegative Ricci curvature
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• A new variational characterization of three-dimensional space forms
• Unnamed Item
• Unnamed Item

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