Statements (61)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:item
|
| gptkbp:bfsLayer |
3
|
| gptkbp:bfsParent |
gptkb:Maryam_Mirzakhani
|
| gptkbp:analyzes |
complex manifolds
|
| gptkbp:can_be |
singularities
automorphisms branch points punctures boundary components |
| gptkbp:constructed_in |
algebraic varieties
complex projective spaces |
| gptkbp:dimensions |
one
|
| gptkbp:example |
two-dimensional manifolds
|
| gptkbp:genus |
a non-negative integer
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann surfaces
|
| gptkbp:is_analyzed_in |
sheaf theory
complex geometry |
| gptkbp:is_connected_to |
moduli spaces
the concept of analytic continuation the concept of conformal mappings the concept of moduli of curves the uniformization theorem |
| gptkbp:is_described_as |
local coordinates
|
| gptkbp:is_equipped_with |
a complex structure
|
| gptkbp:is_fundamental_to |
the study of algebraic geometry
the study of differential equations the study of mathematical logic |
| gptkbp:is_related_to |
the theory of modular forms
Teichmüller theory the theory of elliptic functions the theory of Riemann surfaces |
| gptkbp:is_represented_in |
covering spaces
charts and atlases charts and transition functions |
| gptkbp:is_studied_in |
differential geometry
mathematical physics homology and cohomology |
| gptkbp:is_used_in |
the study of algebraic topology
the study of modular forms the study of quantum field theory the study of algebraic curves the study of complex manifolds the study of complex dynamics the study of complex analysis. the study of non-linear systems the theory of functions of one complex variable |
| gptkbp:map |
the complex plane
|
| gptkbp:named_after |
gptkb:Bernhard_Riemann
|
| gptkbp:related_to |
algebraic geometry
complex analysis |
| gptkbp:scientific_classification |
gptkb:CEO
their topological properties their automorphism groups non-compact their genus and number of punctures |
| gptkbp:supports |
holomorphic functions
meromorphic functions differential forms Riemannian metrics vector bundles |
| gptkbp:used_in |
gptkb:musician
|