S. S. Chern school of differential geometry
E853115
The S. S. Chern school of differential geometry is a mathematical tradition and research lineage in differential geometry founded and shaped by Shiing-Shen Chern and his students, known for its deep contributions to global differential geometry and characteristic classes.
All labels observed (1)
| Label | Occurrences |
|---|---|
| S. S. Chern school of differential geometry canonical | 1 |
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical school
ⓘ
research tradition ⓘ school of differential geometry ⓘ |
| academicDiscipline | mathematics ⓘ |
| associatedWith |
Institute for Advanced Study
NERFINISHED
ⓘ
Mathematical Sciences Research Institute NERFINISHED ⓘ Nankai University NERFINISHED ⓘ University of California, Berkeley NERFINISHED ⓘ University of Chicago NERFINISHED ⓘ |
| field | differential geometry ⓘ |
| founder | Shiing-Shen Chern NERFINISHED ⓘ |
| hasApproach |
coordinate-free formulations
ⓘ
emphasis on intrinsic invariants ⓘ global methods in geometry ⓘ interaction of topology and geometry ⓘ use of differential forms ⓘ |
| hasCoreConcept |
Chern classes
ⓘ
Chern–Simons invariants NERFINISHED ⓘ Chern–Weil theory NERFINISHED ⓘ Finsler geometry ⓘ Gauss–Bonnet type formulas ⓘ Hermitian geometry NERFINISHED ⓘ Riemannian geometry NERFINISHED ⓘ characteristic classes ⓘ complex differential geometry ⓘ connections on fiber bundles ⓘ curvature forms ⓘ geometric analysis ⓘ global differential geometry ⓘ minimal submanifolds ⓘ secondary characteristic classes ⓘ topological invariants ⓘ |
| hasKeyFigure | Shiing-Shen Chern NERFINISHED ⓘ |
| hasKeyTheme |
applications of curvature to topology
ⓘ
construction of canonical geometric structures ⓘ development of intrinsic invariants of manifolds ⓘ global viewpoint on manifolds ⓘ unity of geometry and topology ⓘ |
| influenced |
gauge theory
ⓘ
geometric topology ⓘ mathematical physics ⓘ modern global differential geometry ⓘ theory of characteristic classes ⓘ |
| influencedBy | Shiing-Shen Chern NERFINISHED ⓘ |
| namedAfter | Shiing-Shen Chern NERFINISHED ⓘ |
| subDisciplineOf |
differential topology
ⓘ
geometry ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Shiing-Shen Chern