In this paper, nu-principal cycles of surfaces immersed in R-4 are studied. In terms of geometric invariants, an integral expression for the first derivative of the Poincare mapping associated with a nu-principal cycle is ...

We study some properties of surfaces in 4-space all whose points are umbilic with respect to some normal field. In particular, we show that this condition is equivalent to the orthogonality of the (globally defined) fields ...