Linked from

The 33 pages that link to Tangent space, each with the reason it gives.

• GeodesicRelated: A geodesic begins with a direction chosen in its initial tangent space.

• Differential geometryBroader topic: It lets calculus describe directions and derivatives at points on curved spaces.

• Vector fieldBroader topic: On curved spaces, field vectors belong to the tangent space at each point.

• Lie groupRelated: Tangent vectors near the identity encode infinitesimal group behavior.

• Lagrange multiplierRelated: At an extremum, feasible infinitesimal directions cannot increase the objective.

• Metric tensorBroader topic: The metric assigns an inner product to vectors in each tangent space.

• Differential formRelated: Forms take tangent vectors as inputs and measure oriented infinitesimal directions.

• Riemannian geometryRelated: The metric assigns an inner product to each tangent space.

• Covariant derivativeNarrower topic: Covariant differentiation compares tensor data attached to these pointwise vector spaces.

• Riemann curvature tensorRelated: At each point, curvature acts on tangent vectors and is a multilinear map.

• Riemannian manifoldBroader topic: The metric assigns an inner product separately to each point’s tangent space.

• Riemannian metricBroader topic: The metric assigns an inner product separately to each tangent space.

• Smooth manifoldRelated: Smooth charts let tangent directions be defined consistently across coordinate systems.

• ManifoldBroader topic: Tangent spaces capture the manifold's locally linear behavior at individual points.

• Christoffel symbolsRelated: Each coordinate chart supplies a basis in each tangent space whose variation the symbols encode.

• Lyapunov exponentRelated: Perturbations in this space are evolved to measure trajectory separation.

• Exponential mapNarrower topic: Each exponential map begins with a vector in the tangent space at its base point.

• InfinitesimalRelated: Infinitesimal displacements motivate the local linear structure represented by tangent spaces.

• Tensor fieldRelated: Vectors and covectors in a tensor at a point are drawn from tangent spaces and their duals.

• Exterior derivativeRelated: Differential forms evaluate tangent vectors, giving the exterior derivative its pointwise inputs.

• Level setRelated: At a regular point, its vectors lie in the kernel of the function's derivative.

• Surface normalRelated: The normal direction is defined relative to the tangent directions at the same point.

• Differential topologyRelated: Tangent spaces let smooth maps be analyzed through their derivatives.

• Symplectic geometryRelated: Nondegeneracy is tested by pairing tangent vectors at each point.

• Generalized Stokes theoremRelated: Differential forms act on tangent vectors at each point.

• Riemannian distanceRelated: The metric measures curve velocities in these spaces.

• Affine subspaceCompared with: A tangent space is linear and based at zero; a tangent affine plane is its translated geometric counterpart.

• Principal symbolNarrower topic: Cotangent vectors used by the symbol are dual to tangent directions.

• Symplectic manifoldRelated: The symplectic form is nondegenerate on each tangent space.

• Flow (mathematics)Related: A vector field's value at each point belongs to that point's tangent space.

• Differentiable manifoldBroader topic: Differentiable structure enables tangent vectors to be defined at every point.

• Hairy ball theoremRelated: Each field vector must lie in the sphere's tangent space at its base point.

• Gauss's lemma (differential geometry)Narrower topic: The lemma begins with radial vectors and sphere-tangent vectors in this vector space.