Differential Geometry

Loading...

The apparatus of vector bundles, principal bundles, and connections on bundles plays an extraordinarily important role in modern differential geometry. A smooth manifold always carries a natural vector bundle, the tangent bundle. Loosely speaking, this structure by itself is sufficient only for developing analysis on the manifold, while doing geometry requires, in addition, some way to relate the tangent spaces at different points, i. e. a notion of parallel transport. An important example is provided by affine connections. For a surface in R3, tangent planes at different points can be identified using a natural path-wise parallelism induced by the ambient Euclidean space, which has a well-known standard definition of metric and parallelism. In Riemannian geometry, the Levi-Civita connection serves a similar purpose. (The Levi-Civita connection defines path-wise parallelism in terms of a given arbitrary Riemannian metric on a manifold. ) More generally, differential geometers consider spaces with a vector bundle and an arbitrary affine connection which is not defined in terms of a metric. In physics, the manifold may be the space-time continuum and the bundles and connections are related to various physical fields.

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.

Opinions on Differential geometry

Differential Geometry : Erwin Kreyszig : 9780486667218

Differential geometry - YouTube

Flickr: The Differential Geometry Pool

differential geometry - DriverLayer Search Engine

differential geometry - DriverLayer Search Engine

Differential Geometry : Heinrich W. Guggenheimer ...

Differential Geometry and Its applications issn 1557 5918 ...

Differential geometry three dimensional space

Opinions on Differential geometry

Opinions on Differential geometry

Stephan Tillmann - Differential Geometry MATH3405

differential geometry - DriverLayer Search Engine

Opinions on Differential geometry

Differential geometry three dimensional space

Differential Geometry of Curves and Surfaces, Second ...

Opinions on Differential geometry

differential geometry - DriverLayer Search Engine

MathHistory16: Differential Geometry - YouTube

Book Review: Struik’s Lectures on Classical Differential ...

Thanksgiving Book Review: do Carmo’s Differential Geometry ...

Differential geometry of surfaces - YouTube

packages - Differential geometry add-ons for Mathematica ...

differential geometry - DriverLayer Search Engine

Opinions on Differential geometry

differential geometry - DriverLayer Search Engine

differential geometry - DriverLayer Search Engine

Differential geometry three dimensional space