Displaying similar documents to “On isospectral deformations of riemannian metrics”

Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces

Eugene D. Rodionov, Viktor V. Slavskii (2002)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we investigate one-dimensional sectional curvatures of Riemannian manifolds, conformal deformations of the Riemannian metrics and the structure of locally conformally homogeneous Riemannian manifolds. We prove that the nonnegativity of the one-dimensional sectional curvature of a homogeneous Riemannian space attracts nonnegativity of the Ricci curvature and we show that the inverse is incorrect with the help of the theorems O. Kowalski-S. Nikčevi'c [K-N], D. Alekseevsky-B....