Critical points of the total scalar curvature functional on the space of metrics of constant scalar curvature |
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Authors: | Seungsu Hwang |
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Institution: | Hankuk Aviation University, 200-1 Hwajong-dong, Koyang, Kyonggi-do,?Korea 412-791.?e-mail: seungsu@mail.hangkong.ac.kr, KR
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Abstract: | It is well known that critical points of the total scalar curvature functional ? on the space of all smooth Riemannian structures
of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of ? is restricted to the space of constant scalar curvature metrics, there
has been a conjecture that a critical point is also Einstein or isometric to a standard sphere. In this paper we prove that
n-dimensional critical points have vanishing n− 1 homology under a lower Ricci curvature bound for dimension less than 8.
Received: 12 July 1999 |
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Keywords: | Mathematics Subject Classification (2000): 58E11 53C25 |
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