A functional expression for the curvature of hyper-dimensional Riemannian spaces.
Sarić, Branko (2000)
Lobachevskii Journal of Mathematics
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Displaying similar documents to “On Jacobi fields and a canonical connection in sub-Riemannian geometry”
A functional expression for the curvature of hyper-dimensional Riemannian spaces.
Jacobi Tensors and Ricci Curvature.
John J. O'Sullivan, Jost-Hinrich Eschenburg (1980)
Mathematische Annalen
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The Riemannian curvature tensor and differentiable spaces
Adam Kowalczyk (1984)
Banach Center Publications
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-natural metrics of constant curvature on unit tangent sphere bundles
M. T. K. Abbassi, Giovanni Calvaruso (2012)
Archivum Mathematicum
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We completely classify Riemannian -natural metrics of constant sectional curvature on the unit tangent sphere bundle of a Riemannian manifold . Since the base manifold turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian -natural metric on the unit tangent sphere bundle of a Riemannian surface.
Stanilov-Tsankov-Videv theory.
Brozos-Vázquez, Miguel, Fiedler, Bernd, García-Río, Eduardo, Gilkey, Peter, Nikčević, Stana, Stanilov, Grozio, Tsankov, Yulian, Vázquez-Lorenzo, Ramón, Videv, Veselin (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix
Yana Alexieva, Stefan Ivanov (1999)
Archivum Mathematicum
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Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures , which are not locally homogeneous, in general.