Affine Osserman connections and their Riemann extensions

DOI10.1016/S0926-2245(99)00029-7zbMath0940.53017OpenAlexW2041471686WikidataQ115337410 ScholiaQ115337410MaRDI QIDQ1807643

M. Elena Vázquez-Abal, Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

Publication date: 8 February 2000

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0926-2245(99)00029-7

zbMATH Keywords

Osserman spaceRiemann extension

Mathematics Subject Classification ID

Linear and affine connections (53B05) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (20)

Complete \(k\)-curvature homogeneous pseudo-Riemannian manifolds ⋮ Magnetic curves on cotangent bundles endowed with the Riemann extension ⋮ Two families of affine Osserman connections on 3-dimensional manifolds ⋮ Local obstructions to projective surfaces admitting skew-symmetric Ricci tensor ⋮ Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues ⋮ Euler-Lagrange formulas for pseudo-Kähler manifolds ⋮ Curvature properties of \(\varphi\)-null Osserman Lorentzian \(\mathcal S\)-manifolds ⋮ Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators ⋮ On some differential operators on natural Riemann extensions ⋮ Four-dimensional semi-Riemannian Szabó manifolds ⋮ Homogeneous affine surfaces: affine Killing vector fields and gradient Ricci solitons ⋮ Unnamed Item ⋮ On metric connections with torsion on the cotangent bundle with modified Riemannian extension ⋮ Hermitian-Walker 4-manifolds ⋮ The Riemann extensions with cyclic parallel Ricci tensor ⋮ Analytic continuation, the Chern-Gauss-Bonnet theorem, and the Euler-Lagrange equations in Lovelock theory for indefinite signature metrics ⋮ On Lorentzian spaces of constant sectional curvature ⋮ Unnamed Item ⋮ Geometric realizations of curvature models by manifolds with constant scalar curvature ⋮ Projective affine Osserman curvature models

Cites Work

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• A curvature characterization of certain locally rank-one symmetric spaces
• On a problem of Osserman in Lorentzian geometry
• Two dimensional linear connexions with zero torsion and recurrent curvature
• On the existence of a connection with curvature zero
• Curvature in the Eighties
• Shape Operators of Einstein Hypersurfaces in Indefinite Space Forms
• The inverse problem of the calculus of variations for ordinary differential equations
• Nonsymmetric Osserman indefinite Kähler manifolds
• Nonsymmetric Osserman pseudo-Riemannian manifolds
• ISOPARAMETRIC GEODESIC SPHERES AND A CONJECTURE OF OSSERMAN CONCERNING THE JACOBI OPERATOR

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