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On conformally flat manifolds with constant positive scalar curvature


Author: Giovanni Catino
Journal: Proc. Amer. Math. Soc. 144 (2016), 2627-2634
MSC (2010): Primary 53C20, 53C21
DOI: https://doi.org/10.1090/proc/12925
Published electronically: November 4, 2015
MathSciNet review: 3477081
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Abstract: We classify compact conformally flat $ n$-dimensional manifolds with constant positive scalar curvature and satisfying an optimal integral pinching condition: they are covered isometrically by either $ \mathbb{S}^{n}$ with the round metric, $ \mathbb{S}^{1}\times \mathbb{S}^{n-1}$ with the product metric or $ \mathbb{S}^{1}\times \mathbb{S}^{n-1}$ with a rotationally symmetric Derdzinski metric.


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Additional Information

Giovanni Catino
Affiliation: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Email: giovanni.catino@polimi.it

DOI: https://doi.org/10.1090/proc/12925
Keywords: Conformally flat manifold, rigidity
Received by editor(s): January 6, 2015
Received by editor(s) in revised form: August 6, 2015
Published electronically: November 4, 2015
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society