Abstract
By the work of [CG2] and [CG3], the Riemannian manifolds whose injectivity radii are small everywhere relative to the bound on sectional curvature admit positive rank F-structures. We will prove, in dimension four, that if the volumes of the manifolds are also smaller than a positive constant, then the manifolds actually admit polarized F-structures. In particular, this result implies an affirmative answer to the Gromov's Gap conjecture on vanishing minimal volume in dimension four.
Original language | English (US) |
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Pages (from-to) | 474-501 |
Number of pages | 28 |
Journal | Geometric and Functional Analysis |
Volume | 3 |
Issue number | 5 |
DOIs | |
State | Published - Sep 1993 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Geometry and Topology