Nonnegatively and Positively curved manifolds
Burkhard Wilking
TL;DR
This survey reviews the current state of research on manifolds with nonnegative and positive curvature, highlighting key results, open problems, and recent developments in differential geometry.
Contribution
It compiles and discusses recent advances and open questions regarding the geometry and topology of nonnegatively and positively curved manifolds.
Findings
Summary of classification results for positively curved manifolds
Discussion of topological constraints imposed by curvature conditions
Overview of recent progress and open problems in the field
Abstract
This is a survey written for a special edition of the journal of differential geometry.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology