A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ1= ρ2≠ ρ3

DOI10.1017/S002776300000461XzbMath0788.53038OpenAlexW1925811826WikidataQ115336460 ScholiaQ115336460MaRDI QIDQ4278762

Oldřich Kowalski

Publication date: 7 March 1994

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s002776300000461x

zbMATH Keywords

constant principal Ricci curvatureshomogeneous Riemannian 3-manifold

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25)

Related Items (17)

Non-homogeneous relatives of symmetric spaces ⋮ Riemannian manifolds whose curvature operator R(X, Y) has constant eigenvalues ⋮ Three-dimensional Riemannian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3 ⋮ On Riemannian 3-manifolds with distinct constant Ricci eigenvalues ⋮ On curvature homogeneous three-dimensional Lorentzian manifolds ⋮ On \(\mathcal {M}\)-projectively semisymmetric Lorentzian \(\alpha \)-Sasakian manifolds ⋮ Special ball-homogeneous spaces ⋮ On Ricci eigenvalues of locally homogeneous Riemann 3-manifolds ⋮ Existence and classification of three-dimensional Lorentzian manifolds with prescribed distinct Ricci eigenvalues ⋮ Riemannian 3-metrics with a generic Codazzi Ricci tensor ⋮ Three-dimensional Lorentzian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3 ⋮ Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues ⋮ Three-dimensional Ivanov–Petrova manifolds ⋮ Hypersurfaces with a parallel higher fundamental form ⋮ Curvature properties of Gödel metric ⋮ On curvature-homogeneous spaces of type (1,3) ⋮ The third fundamental form metric for hypersurfaces in nonflat space forms

Cites Work

• Cliffordalgebren und neue isoparametrische Hyperflächen
• Existence of metrics with prescribed Ricci curvature: Local theory
• Curvature homogeneous spaces with a solvable Lie group as homogeneous model
• On curvature homogeneity of Riemannian manifolds
• Curvatures of left invariant metrics on Lie groups
• Curvature homogeneous riemannian manifolds
• A characterization of locally homogeneous Riemann manifolds of dimension 3

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