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...

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...

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...

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...

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

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

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...

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...

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

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

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, a smooth surface in three dimensions has a ridge point when a line of curvature has a local maximum or minimum of principal curvature...

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}}...

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...

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...

(2007). "Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups". Journal of Differential Geometry. 76 (3): 399–422. arXiv:math...

mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects such...

the above formulas also hold for immersions. In classical differential geometry of surfaces, the Codazzi–Mainardi equations are expressed via the second...

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...

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 differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a...

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...

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...

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...

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