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Displaying similar documents to “Remark on a conjecture of conformal transformations of Riemannian manifolds”

Conformal gradient vector fields on a compact Riemannian manifold

Sharief Deshmukh, Falleh Al-Solamy (2008)

Colloquium Mathematicae

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It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying 0 < Ric ≤ (n-1)(2-nc/λ₁)c for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold...

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....