Remarks concerning the conformal deformation of riemannian structures on compact manifolds
Neil S. Trudinger (1968)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Remarks concerning the conformal deformation of riemannian structures on compact manifolds
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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...
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