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Certain conditions for a Riemannian manifold to be isometric with a sphere:Dedicated to Professor Kentaro Yano on his fiftieth birthday
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This article is published in Tokyo Sugaku Kaisya Zasshi.The article was published on 1962-01-01 and is currently open access. It has received 511 citations till now. The article focuses on the topics: Riemannian manifold.read more
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Sasaki-Einstein manifolds and volume minimisation
TL;DR: In this paper, it was shown that the volume function of a Sasaki-Einstein manifold is a function on the space of Reeb vector fields, and that it can be computed in terms of topological fixed point data.
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Conformal geometry, contact geometry, and the calculus of variations
TL;DR: In this article, the Yamabe problem was studied in the conformal class of unit volume metrics, where the tensor is viewed as an endomorphism of the tangent bundle and σk d notes the trace of the induced map on the kth exterior power.
Journal ArticleDOI
The scalar curvature equation on 2- and 3-spheres
TL;DR: In this paper, the authors obtained a priori estimates for solutions to the prescribed scalar curvature equation on 2-and 3-spheres under a nondegeneracy assumption on the curvature function.
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Extremal metrics of zeta function determinants on 4-manifolds
Sun-Yung Alice Chang,Paul Yang +1 more
TL;DR: In conformal geometry, the Sobolev inequality at a critical exponent has received much attention as mentioned in this paper, and the determination of the best constants has played a crucial role in the Yamabe problem.
Surveys in differential geometry
TL;DR: In this article, the authors survey the recent progress made on estimating positive eigenvalues of Laplacian on hyperbolic Riemann surfaces in the case of congruence subgroups in connection with the Selberg conjecture, as well as certain related ones.
References
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Journal ArticleDOI
Sasaki-Einstein manifolds and volume minimisation
TL;DR: In this paper, it was shown that the volume function of a Sasaki-Einstein manifold is a function on the space of Reeb vector fields, and that it can be computed in terms of topological fixed point data.
Journal ArticleDOI
Conformal geometry, contact geometry, and the calculus of variations
TL;DR: In this article, the Yamabe problem was studied in the conformal class of unit volume metrics, where the tensor is viewed as an endomorphism of the tangent bundle and σk d notes the trace of the induced map on the kth exterior power.