Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing

Shaosai Huang ; Xiaochun Rong ; Bing Wang

Symmetry, integrability and geometry: methods and applications, Tome 16 (2020)

Résumé

We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques. We then prove that if a Calabi–Yau manifold is sufficiently volume collapsed with bounded diameter and sectional curvature, then it admits a Ricci-flat Kähler metric together with a compatible pure nilpotent Killing structure: this is related to an open question of Cheeger, Fukaya and Gromov.

Détail

Keywords: almost flat manifold, collapsing geometry, locally bounded Ricci covering geometry, nilpotent Killing structure, Ricci flow.

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