Statements (70)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:architecture
|
| gptkbp:analyzes |
complex projective line
|
| gptkbp:can |
automorphisms
branch points finite genus infinite genus |
| gptkbp:can_be_mapped_to |
complex plane
Riemann sphere |
| gptkbp:constructed_in |
topological spaces
algebraic curves covering spaces |
| gptkbp:exhibits |
singularities
complex behavior multiple sheets |
| gptkbp:has_topology |
complex manifold
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann surface
|
| gptkbp:is_a |
gptkb:item
complex manifold geometric object two-dimensional manifold |
| gptkbp:is_associated_with |
conformal mappings
|
| gptkbp:is_atype_of |
gptkb:topology
analytic space differentiable manifold |
| gptkbp:is_characterized_by |
gptkb:genus
local coordinates branch cuts holomorphic transitions |
| gptkbp:is_connected_to |
algebraic topology
differential equations complex manifolds complex structures holomorphic functions Riemann surfaces of higher genus complex analysis techniques |
| gptkbp:is_essential_for |
gptkb:topology
|
| gptkbp:is_fundamental_to |
theory of functions
theory of complex functions theory of algebraic curves theory of Riemann surfaces |
| gptkbp:is_related_to |
sheaf theory
topological invariants analytic continuation moduli space Riemann-Roch theorem moduli of curves |
| gptkbp:is_represented_in |
charts and atlases
|
| gptkbp:is_studied_in |
differential geometry
mathematical physics mathematical logic complex geometry mathematical physics research |
| gptkbp:is_used_in |
gptkb:Physics
gptkb:string_theory computational mathematics mathematical modeling number theory mathematical analysis mathematical research |
| gptkbp:length |
one
|
| gptkbp:model |
complex variables
|
| gptkbp:named_after |
gptkb:Bernhard_Riemann
|
| gptkbp:related_to |
complex analysis
|
| gptkbp:scientific_classification |
Riemann-Hurwitz formula
|
| gptkbp:support |
meromorphic functions
differentiable structures non-constant meromorphic functions |
| gptkbp:used_in |
algebraic geometry
|
| gptkbp:bfsParent |
gptkb:Klein's_quartic
|
| gptkbp:bfsLayer |
5
|