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Some notes on drawing twofolds in 4-dimensional Euclidean space. (English) Zbl 1178.53007
Summary: In the present paper we give an elementary and illustrative proof that in \(\mathbb E^4\), the complete surfaces with constant positive curvature are not isomorphic. It is well-known that if two surfaces in \(\mathbf E^3\) are complete with the same positive curvature they are globally isomorphic. The same statement is not true in \(\mathbb E^4\), although these surfaces remain global isometric. We will illustrate our proof with some nice examples.

53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53A05 Surfaces in Euclidean and related spaces
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)