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Displaying similar documents to “Constant scalar curvature metrics on connected sums.”

Conformal gradient vector fields on a compact Riemannian manifold

Sharief Deshmukh, Falleh Al-Solamy (2008)

Colloquium Mathematicae

Similarity:

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...