Manifolds

This is the Sage implementation of manifolds resulting from the SageManifolds project. This section describes only the “manifold” part of SageManifolds; the pure algebraic part is described in the section Tensors on free modules of finite rank.

More documentation (in particular example worksheets) can be found here.

• Topological Manifolds
  • Topological Manifolds
  • Subsets of Topological Manifolds
  • Manifold Structures
  • Points of Topological Manifolds
  • Coordinate Charts
    • Coordinate Charts
    • Chart Functions
    • Coordinate calculus methods
  • Scalar Fields
    • Algebra of Scalar Fields
    • Scalar Fields
  • Continuous Maps
    • Sets of Morphisms between Topological Manifolds
    • Continuous Maps Between Topological Manifolds
    • Images of Manifold Subsets under Continuous Maps as Subsets of the Codomain
  • Submanifolds of topological manifolds
  • Topological Vector Bundles
    • Topological Vector Bundle
    • Vector Bundle Fibers
    • Vector Bundle Fiber Elements
    • Trivializations
    • Local Frames
    • Section Modules
    • Sections
  • Families of Manifold Objects
  • Topological Closures of Manifold Subsets
  • Manifold Subsets Defined as Pullbacks of Subsets under Continuous Maps
• Differentiable Manifolds
  • Differentiable Manifolds
  • Coordinate Charts on Differentiable Manifolds
  • The Real Line and Open Intervals
  • Scalar Fields
    • Algebra of Differentiable Scalar Fields
    • Differentiable Scalar Fields
  • Differentiable Maps and Curves
    • Sets of Morphisms between Differentiable Manifolds
    • Differentiable Maps between Differentiable Manifolds
    • Curves in Manifolds
    • Integrated Curves and Geodesics in Manifolds
  • Tangent Spaces
    • Tangent Spaces
    • Tangent Vectors
  • Vector Fields
    • Vector Field Modules
    • Vector Fields
    • Vector Frames
    • Group of Tangent-Space Automorphism Fields
    • Tangent-Space Automorphism Fields
  • Tensor Fields
    • Tensor Field Modules
    • Tensor Fields
    • Tensor Fields with Values on a Parallelizable Manifold
  • Differential Forms
    • Differential Form Modules
    • Differential Forms
  • Mixed Differential Forms
    • Graded Algebra of Mixed Differential Forms
    • Mixed Differential Forms
  • De Rham Cohomology
  • Alternating Multivector Fields
    • Multivector Field Modules
    • Multivector Fields
  • Affine Connections
  • Submanifolds of differentiable manifolds
  • Differentiable Vector Bundles
    • Differentiable Vector Bundles
    • Bundle Connections
    • Characteristic Classes
• Pseudo-Riemannian Manifolds
  • Pseudo-Riemannian Manifolds
  • Euclidean Spaces
    • Euclidean Spaces
    • Spheres smoothly embedded in Euclidean Space
    • Operators for vector calculus
  • Pseudo-Riemannian Metrics and Degenerate Metrics
  • Levi-Civita Connections
  • Pseudo-Riemannian submanifolds
  • Degenerate Metric Manifolds
    • Degenerate manifolds
    • Degenerate submanifolds
• Utilities for Calculus
• Manifolds Catalog

Indices and Tables

• Index

• Module Index

• Search Page