Treatise of Physics

Knowledge graph › Differentiable Manifolds, Tensors, and Curvature

proposition 13.56 Product manifold

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2695 · p. 485

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proposition 13.56: Product manifold13.56definition 13.44: Atlas13.44definition 13.43: Coordinate system13.43definition 13.48: Differentiable manifold13.48example 13.57: The cylinder13.57proof : ch:11-manifolds-tensors-curvature@proof-9proofdefinition A.299: Manifold with boundaryA.299definition A.302: OrientationA.302definition 13.45: Differentiable map on a topological space13.45definition 13.47: Differentiable structure13.47definition 13.49: Smooth map between manifolds13.49proposition 13.46: Compatibility of atlases13.46definition A.67: Symplectic manifoldA.67definition 13.71: Differentiable curve13.71definition 13.66: Smooth action; free; proper; orbit13.66definition 13.117: Metric tensor of signature (p,q)13.117definition 13.54: Embedded submanifold13.54definition 13.81: Vector on a manifold13.81

Edges

typedirectionnode provenancewhere
depends_on → Atlas declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2711
depends_on → Coordinate system declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2711
depends_on → Differentiable manifold declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2711
depends_on ← The cylinder declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2749
proves ← ch:11-manifolds-tensors-curvature@proof-9 declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2714