Conformality and isometry of Riemannian manifolds to spheres

Hsiung, Chuan-chih; Stern, Louis W.

doi:10.1090/S0002-9947-1972-0284948-4

Conformality and isometry of Riemannian manifolds to spheres
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by Chuan-chih Hsiung and Louis W. Stern PDF

Trans. Amer. Math. Soc. 163 (1972), 65-73 Request permission

Abstract:

Suppose that a compact Riemannian manifold ${M^n}$ of dimension $n > 2$ admits an infinitesimal nonisometric conformal transformation $\upsilon$. Some curvature conditions are given for ${M^n}$ to be conformal or isometric to an $n$-sphere under the initial assumption that ${L_\upsilon }R = 0$, where ${L_\upsilon }$ is the operator of the infinitesimal transformation $\upsilon$ and $R$ is the scalar curvature of ${M^n}$. For some special cases, these conditions were given by Yano [10] and Hsiung [2].

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