::Differential geometry


Geometry::manifold    Geometry::space    Which::complex    Metric::title    Study::curves    First::surfaces

A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines.

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.

Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds. Differential geometry is closely related to differential topology and the geometric aspects of the theory of differential equations. The differential geometry of surfaces captures many of the key ideas and techniques characteristic of this field.

Differential geometry sections
Intro   History of Development    Branches of differential geometry    Bundles and connections    Intrinsic versus extrinsic    Applications   See also   References    Further reading    External links   

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