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)|
|Number of pages||28|
|Journal||Geometric and Functional Analysis|
|State||Published - Sep 1993|
All Science Journal Classification (ASJC) codes
- Geometry and Topology