Abstract
Saddle surfaces are the generalization of surfaces of negative Gaussian curvature. A part of arbitrary surface of three-dimensional Euclidean space cut off by arbitrary plane with compact form closure of a contour section is called a crust. If we cannot cut off a crust by any plane, then this surface is a saddle surface. For a twice continuously differentiable surface to be a saddle surface, it is necessary and sufficient that at each point of the surface its Gaussian curvature is nonpositive. There are no closed surfaces among saddle surfaces in E 3.
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© 2015 Springer International Publishing Switzerland
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Krivoshapko, S.N., Ivanov, V.N. (2015). Saddle Surfaces. In: Encyclopedia of Analytical Surfaces. Springer, Cham. https://doi.org/10.1007/978-3-319-11773-7_33
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DOI: https://doi.org/10.1007/978-3-319-11773-7_33
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Publisher Name: Springer, Cham
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