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

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...

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...

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

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...

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

open subset of the Euclidean plane (see Surface (topology) and Surface (differential geometry)). This allows defining surfaces in spaces of dimension higher...

surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of...

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...

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...

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

intersection of algebraic geometry, differential geometry, and complex analysis, and uses tools from all three areas. Because of the blend of techniques...

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

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

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

CUP Archive, 1954. Carmo, Manfredo Perdigão do (1976). Differential geometry of curves and surfaces. Vol. 2. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-212589-7...

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...

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

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

Springer Encyclopedia of Mathematics, Weingarten derivational formulas Struik, Dirk J. (1988), Lectures on Classical Differential Geometry, Dover Publications...

characterized by the volume of infinitesimally small geodesic balls. In the context of the differential geometry of surfaces, the scalar curvature is twice...

hyperbolic case. In the differential geometry of surfaces, the question of a triangle's angular defect is understood as a special case of the Gauss-Bonnet theorem...

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

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

doi:10.1007/s00004-011-0087-z Do Carmo, Manfredo P. : Differential Geometry of Curves and Surfaces, Prentice-Hall; 1 edition, 1976 ISBN 978-0132125895 Barth...