Manifold Structures¶
These classes encode the structure of a manifold.
AUTHORS:
- Travis Scrimshaw (2015-11-25): Initial version
- Eric Gourgoulhon (2015): add
DifferentialStructureandRealDifferentialStructure - Eric Gourgoulhon (2018): add
PseudoRiemannianStructure,RiemannianStructureandLorentzianStructure
-
class
sage.manifolds.structure.DifferentialStructure¶ Bases:
sage.misc.fast_methods.SingletonThe structure of a differentiable manifold over a general topological field.
-
chart¶
-
scalar_field_algebra¶ alias of
sage.manifolds.differentiable.scalarfield_algebra.DiffScalarFieldAlgebra
-
subcategory(cat)¶ Return the subcategory of
catcorresponding to the structure ofself.EXAMPLES:
sage: from sage.manifolds.structure import DifferentialStructure sage: from sage.categories.manifolds import Manifolds sage: DifferentialStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-
-
class
sage.manifolds.structure.LorentzianStructure¶ Bases:
sage.misc.fast_methods.SingletonThe structure of a Lorentzian manifold.
-
chart¶
-
scalar_field_algebra¶ alias of
sage.manifolds.differentiable.scalarfield_algebra.DiffScalarFieldAlgebra
-
subcategory(cat)¶ Return the subcategory of
catcorresponding to the structure ofself.EXAMPLES:
sage: from sage.manifolds.structure import LorentzianStructure sage: from sage.categories.manifolds import Manifolds sage: LorentzianStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-
-
class
sage.manifolds.structure.PseudoRiemannianStructure¶ Bases:
sage.misc.fast_methods.SingletonThe structure of a pseudo-Riemannian manifold.
-
chart¶
-
scalar_field_algebra¶ alias of
sage.manifolds.differentiable.scalarfield_algebra.DiffScalarFieldAlgebra
-
subcategory(cat)¶ Return the subcategory of
catcorresponding to the structure ofself.EXAMPLES:
sage: from sage.manifolds.structure import PseudoRiemannianStructure sage: from sage.categories.manifolds import Manifolds sage: PseudoRiemannianStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-
-
class
sage.manifolds.structure.RealDifferentialStructure¶ Bases:
sage.misc.fast_methods.SingletonThe structure of a differentiable manifold over \(\RR\).
-
chart¶
-
scalar_field_algebra¶ alias of
sage.manifolds.differentiable.scalarfield_algebra.DiffScalarFieldAlgebra
-
subcategory(cat)¶ Return the subcategory of
catcorresponding to the structure ofself.EXAMPLES:
sage: from sage.manifolds.structure import RealDifferentialStructure sage: from sage.categories.manifolds import Manifolds sage: RealDifferentialStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-
-
class
sage.manifolds.structure.RealTopologicalStructure¶ Bases:
sage.misc.fast_methods.SingletonThe structure of a topological manifold over \(\RR\).
-
chart¶ alias of
sage.manifolds.chart.RealChart
-
homset¶ alias of
sage.manifolds.manifold_homset.TopologicalManifoldHomset
-
scalar_field_algebra¶ alias of
sage.manifolds.scalarfield_algebra.ScalarFieldAlgebra
-
subcategory(cat)¶ Return the subcategory of
catcorresponding to the structure ofself.EXAMPLES:
sage: from sage.manifolds.structure import RealTopologicalStructure sage: from sage.categories.manifolds import Manifolds sage: RealTopologicalStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-
-
class
sage.manifolds.structure.RiemannianStructure¶ Bases:
sage.misc.fast_methods.SingletonThe structure of a Riemannian manifold.
-
chart¶
-
scalar_field_algebra¶ alias of
sage.manifolds.differentiable.scalarfield_algebra.DiffScalarFieldAlgebra
-
subcategory(cat)¶ Return the subcategory of
catcorresponding to the structure ofself.EXAMPLES:
sage: from sage.manifolds.structure import RiemannianStructure sage: from sage.categories.manifolds import Manifolds sage: RiemannianStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-
-
class
sage.manifolds.structure.TopologicalStructure¶ Bases:
sage.misc.fast_methods.SingletonThe structure of a topological manifold over a general topological field.
-
chart¶ alias of
sage.manifolds.chart.Chart
-
homset¶ alias of
sage.manifolds.manifold_homset.TopologicalManifoldHomset
-
scalar_field_algebra¶ alias of
sage.manifolds.scalarfield_algebra.ScalarFieldAlgebra
-
subcategory(cat)¶ Return the subcategory of
catcorresponding to the structure ofself.EXAMPLES:
sage: from sage.manifolds.structure import TopologicalStructure sage: from sage.categories.manifolds import Manifolds sage: TopologicalStructure().subcategory(Manifolds(RR)) Category of manifolds over Real Field with 53 bits of precision
-