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I'm currently at a Differential Geometry meeting and there is a mini-course on positively curved Riemannian manifolds. There, we were told that a technique to construct such manifolds is a Cheeger deformation, which (if I understood correctly) is a generalization of a one-parameter family of surfaces of revolution given by $\frac{f}{\lambda f + 1}$, where $f$ is the curve that generates a surface of revolution in Euclidean space and $\lambda$ is a positive parameter that varies over $[0,\infty)$. Can anyone tell me what is the concrete definition of a Cheeger deformation and how are they used to construct manifolds of positive (or non-negative, perhaps; I don't remember) curvature? Thanks a lot.

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Did you try googling "Cheeger deformation"? –  Deane Yang Dec 11 '10 at 0:55
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And the first hit is now amazingly enough this question! –  José Figueroa-O'Farrill Dec 11 '10 at 1:35
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See W. Ziller's survey available on his web page: math.upenn.edu/~wziller/papers/survey_noneg_curvature_Final.pdf On page 3 he defines Cheeger deformations, and more follows. –  Dan Fox Dec 11 '10 at 12:52

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