# Definition:Differential Geometry

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## Definition

**Differential geometry** is a branch of mathematics which uses techniques from calculus and linear algebra to study problems in geometry.

It is concerned with the intrinsic properties of curves and surfaces as found using differential calculus.

## Also see

- Results about
**differential geometry**can be found**here**.

## Historical Note

The subject of **differential geometry** was originated by Carl Friedrich Gauss who in $1827$ defined what is now called the Gaussian curvature of a surface at a point.

He provided formulas for this in terms of the partial derivatives using a number of different coordinate systems.

This was extended by Bernhard Riemann to a general type of space with arbitrary dimensions.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**differential geometry** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**differential geometry**