Cotangent bundle

Related lectures (14)

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Explores the definition, properties, and geometric interpretations of tangent and cotangent functions in trigonometry.

Introduces one-forms, tensors, normal coordinates, and metric tensors in differential geometry.

Explores the symmetries and properties of tangent and cotangent functions with different angles.

Covers the computation of matrices for mesh processing and the Laplace equation solution for mesh deformation.

Covers smooth maps, vector fields, and retractions on manifolds, emphasizing the importance of smoothly varying curves.

Delves into tangent vectors as equivalence classes on manifolds, highlighting their abstract nature and role in optimization.

Explores surfaces with variable curvature, constant curvature, and gothic surfaces, as well as singularities and the inversion of normals.

Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

Explores the properties of tangent and cotangent functions, including domains and periodicity.

Explains the relations in a right-angled triangle involving trigonometric functions.

Explores trigonometric addition theorem, double angles, and tangent properties.

Explores solving trigonometric equations with tangent and cotangent functions, along with arctangent and arccotangent definitions.

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