In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...

and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during...

on which Geometry is Based"). It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian...

Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are...

In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed...

mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical...

field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal...

In three dimensions all developable surfaces are ruled surfaces (but not vice versa). There are developable surfaces in four-dimensional space ⁠ R 4 {\displaystyle...

In differential geometry, constant-mean-curvature (CMC) surfaces are surfaces with constant mean curvature. This includes minimal surfaces as a subset...

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal...

In differential geometry a translation surface is a surface that is generated by translations: For two space curves c 1 , c 2 {\displaystyle c_{1},c_{2}}...

1007/s00004-011-0087-z do Carmo, Manfredo P. (1976), Differential Geometry of Curves and Surfaces (1st ed.), Prentice-Hall, ISBN 978-0132125895 Barth,...

This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics...

Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. The theorem says that...

on the surface. M. do Carmo, Differential Geometry of Curves and Surfaces, page 257. Andrew Pressley (2001). Elementary Differential Geometry. Springer...

Halle-Wittenberg. He made some important contributions to the differential geometry of surfaces, such as the Weingarten equations. Julius Weingarten at the...

contributions to the differential geometry of surfaces, such as the Codazzi–Mainardi equations. He graduated in mathematics at the University of Pavia, where...

In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame...

In geometry, a pseudosphere is a surface with constant negative Gaussian curvature. A pseudosphere of radius R is a surface in R 3 {\displaystyle \mathbb...

H {\displaystyle H} of a surface S {\displaystyle S} is an extrinsic measure of curvature that comes from differential geometry and that locally describes...

In the differential geometry of surfaces, an asymptotic curve is a curve always tangent to an asymptotic direction of the surface (where they exist). It...

the mathematical study of the differential geometry of surfaces, a tangent developable is a particular kind of developable surface obtained from a curve...

hyperbolic paraboloid shape. Saddle surfaces have negative Gaussian curvature which distinguish them from convex/elliptical surfaces which have positive Gaussian...

theory of connections. After the classical work of Gauss on the differential geometry of surfaces and the subsequent emergence of the concept of Riemannian...

closely related with other notions of entropy found in dynamical systems and plays an important role in differential geometry and geometric group theory. If...

In the differential geometry of surfaces, the Monge patch designates the parameterization of a surface by its height over a flat reference plane. It is...

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential...

mathematician. He made some important contributions to the differential geometry of surfaces, including the Gauss–Bonnet theorem. Pierre Bonnet attended...

frequently arise in differential geometry, for example, in the Weyl and Minkowski problems in differential geometry of surfaces. They were first studied...

In the mathematical field of differential geometry, the Simons formula (also known as the Simons identity, and in some variants as the Simons inequality)...