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Conformally warped manifolds and quasi-Einstein metrics
Conformally warped manifolds quasi-Einstein metrics
2010/11/18
Smooth metric measure spaces have been studied from the two different perspectives of Bakry-\'Emery and Chang-Gursky-Yang, both of which are closely related to work of Perelman on the Ricci flow. The...
Convergence of vector bundles with metrics of Sasaki-type
Convergence vector bundles metrics of Sasaki-type
2010/11/9
If a sequence of Riemannian manifolds, $X_i$, converges in the pointed Gromov-Hausdorff sense to a limit space, $X_\infty$, and if $E_i$ are vector bundles over $X_i$ endowed with metrics of Sasaki-t...
In this paper we prove that given a smoothly conformally compact metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact. We apply recent results of Schn\"ur...
On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$
Einstein metrics normalized Ricci flow and smooth structures
2010/11/30
Recent years have witnessed a drastic increase in our understanding of the topology and geometry of 4-manifolds and complex surfaces. The newest developments can be exemplified by the construction of ...