THE STRUCTURE OF ALGEBRAIC COVARIANT DERIVATIVE CURVATURE TENSORS

DOI10.1142/S0219887804000356zbMath1080.53017arXivmath/0404060OpenAlexW3102968183MaRDI QIDQ4659678

Peter B. Gilkey, Eduardo García-Río, Bernd Fiedler, José Carlos Díaz-Ramos

Publication date: 21 March 2005

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404060

zbMATH Keywords

algebraic curvature tensorJacobi operatorskew-symmetric curvature operatorNash embedding theoremalgebraic covariant derivative tensorSzabó operator.

Mathematics Subject Classification ID

Local Riemannian geometry (53B20)

Related Items (5)

Geometry of manifolds with area metric: multi-metric backgrounds ⋮ Maximal domains of radial harmonic functions ⋮ Unnamed Item ⋮ Covariant derivative of the curvature tensor of pseudo-Kählerian manifolds ⋮ CURVATURE STRUCTURE OF SELF-DUAL 4-MANIFOLDS

Cites Work

• The imbedding problem for Riemannian manifolds
• A curvature characterization of certain locally rank-one symmetric spaces
• A short topological proof for the symmetry of 2 point homogeneous spaces
• On a problem of Osserman in Lorentzian geometry
• Two theorems on Osserman manifolds.
• A note on the structure of algebraic curvature tensors
• Applications of algebraic topology in bounding the rank of the skew-symmetric curvature operator
• Curvature in the Eighties
• CURVATURE TENSORS WHOSE JACOBI OR SZABÓ OPERATOR IS NILPOTENT ON NULL VECTORS
• Complete curvature homogeneous pseudo-Riemannian manifolds
• Osserman manifolds in semi-Riemannian geometry

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