Differential geometry of surfaces

two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space

stationary point that is not a local extremum

surface through every point of which runs a straight line which equally is on the surface

surface that locally minimizes its area

In geometry, a pseudosphere is a surface in \mathbb{R}^3. It is the most famous example of a pseudospherical surface. A pseudospherical surface is a surface piecewise smoothly immersed in \mathbb{R}^3 with constant negative Gaussian curvature. A "pseudospherical surface of radius " is a surface in \mathbb{R}^3 having curvature −1/R2 at each point. Its name comes from the analogy with the sphere of radius , which is a surface of curvature 1/R2. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface.

product of the principal curvatures of a surface

"Remarkable theorem" about Gauss' curvature as an invariant

at a given point of a surface, one of the two eigenvalues of the shape operator at the point

in differential geometry, an extrinsic measure of curvature of a surface

quadratic form related to curvatures of surfaces

in differential geometry, a function that maps each point in a surface to its normal direction

deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric

compact Riemann surface of genus 3

theorem in the mathematical field of differential geometry

concept in differential geometry

Natural moving frame in differential geometry of surfaces

genus-7 Hurwitz surface

conic section which describes the local shape of a surface

locally spherical point on a mathematical surface

equations used in vector calculus

formula in classical differential geometry

steepest slope on a surface

Fundamental formulas linking the metric and curvature tensor of a manifold