Closed principal lines of surfaces immersed in the Euclidean 4-space
A closed principal curvature line on a surface \(M\) immersed in Euclidean 3-space is called a principal cycle. In the first part the authors give a definition of \(v\)-principal cycles in the case of a surface \(M\) immersed in Euclidean 4-space; hereby in \(p\in M\) it is \(v\in (T_pM)^\perp\). The main theorem gives an expression of the first derivative of Poincaré's map associated to a \(v\)-principal cycle by geometric invariants. The final part gives examples related to ruled surfaces and tubes.
scientific article; zbMATH DE number 1845274