Displaying similar documents to “On Jacobi fields and a canonical connection in sub-Riemannian geometry”

g -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 g -natural metrics of constant sectional curvature on the unit tangent sphere bundle T 1 M of a Riemannian manifold ( M , g ) . Since the base manifold M turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian g -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 r 1 = r 2 = 0 , r 3 ≠ 0 , which are not locally homogeneous, in general.