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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conformality and isometry of Riemannian manifolds to spheres


Authors: Chuan-chih Hsiung and Louis W. Stern
Journal: Trans. Amer. Math. Soc. 163 (1972), 65-73
MSC: Primary 53.72
DOI: https://doi.org/10.1090/S0002-9947-1972-0284948-4
MathSciNet review: 0284948
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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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DOI: https://doi.org/10.1090/S0002-9947-1972-0284948-4
Keywords: Infinitesimal nonisometric conformal transformations, scalar curvature, lengths of Riemann and Ricci curvature tensors
Article copyright: © Copyright 1972 American Mathematical Society