Geometry III pp 179-250 | Cite as

Local Theory of Bendings of Surfaces

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 48)


The origin of the theory of bendings as one of the basic problems of metrical geometry is associated with the names of Euler, Lagrange, Legendre, Cauchy and Gauss. After it was discovered that on surfaces there is an “intrinsic geometry” that does not depend on the external form of the surface, there naturally arose the question of the possibility of deforming the surface, preserving its intrinsic geometry. Consideration of isometric immersions (or, as we say, realizations) of abstractly given Riemannian metrics also leads to the problem of bendings of surfaces as to some problem about the uniqueness or non-uniqueness of an immersion.


Configuration Space Local Theory Convex Surface Positive Curvature Isometric Immersion 
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