Displaying similar documents to “Metric of special 2F-flat Riemannian spaces”

On some relations between curvature and metric tensors in Riemannian spaces

Mikeš, Josef, Laitochová, Jitka, Pokorná, Olga

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The paper generalizes results of and [Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 295-296 (1996; Zbl 0895.53038) and Sib. Mat. Zh. 39, No. 4, 1005-1012 (1998; Zbl 0913.53019)] on the existence and uniqueness of a Riemannian metric on a domain in ℝ n given prescribed values for some of the components of the Riemann curvature tensor and initial values of the metric and its partial derivatives. The authors establish the construction (existence and uniqueness) of a metric tensor g i j in...

φ ( Ric ) -vector fields in Riemannian spaces

Irena Hinterleitner, Volodymyr A. Kiosak (2008)

Archivum Mathematicum

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In this paper we study vector fields in Riemannian spaces, which satisfy ∇ ϕ = μ , 𝐑𝐢𝐜 , μ = const. We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and ϕ ( Ric ) -vector fields cannot exist simultaneously. It was found that Riemannian spaces with ϕ ( Ric ) -vector fields of constant length have constant scalar curvature. The conditions for the existence of ϕ ( Ric ) -vector fields in symmetric spaces...