Definition:Gaussian Curvature

Definition

The Gaussian curvature $\Kappa$ of a surface at a point is the product of the principal curvatures, $\kappa_1$ and $\kappa_2$, at the given point:

$\Kappa = \kappa_1 \kappa_2$

Also known as

The Gaussian curvature of a surface at a point is also known as the Gauss curvature.

Some sources refer to it as the total curvature.

Also see

• Results about Gaussian curvature can be found here.

Source of Name

This entry was named for Carl Friedrich Gauss.

Historical Note

The concept of Gaussian curvature was developed by Carl Friedrich Gauss in his $1827$ work Disquisitiones Generales circa Superficies Curvas.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Gaussian curvature
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): curvature
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Gaussian curvature
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Riemannian geometry
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Gaussian curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Riemannian geometry