This survey starts with the historical landmarks leading to the study of principal
configurations on surfaces, their structural stability and further generalizations. Here it is …

To every positive ${C^ r} $-quadratic differential form defined on an oriented two manifold is
associated a pair of transversal one-dimensional ${C^ r} $-foliations with common …

In this paper are studied immersions of surfaces into to R 3 whose nets of asymptotic lines
are topologically undisturbed under small perturbations of the immersion. These immersions …

The notion of principal configuration of immersions of surfaces into ℝ³, due to Sotomayor
and Gutierrez [16] for lines of curvature and umbilics, is extended to that of mean directional …

The simplest patterns of qualitative changes on the configurations of lines of principal
curvature around umbilic points on surfaces whose immersions into ℝ 3 depend smoothly …

If\(\mathcal {D}\) is the set of self-diffeomorphisms of a compact smooth manifold\(M\,\)
and\(\mathcal {D}\) is equipped with the\(C^{1}\) topology then\(f\in\mathcal {D}\) is …

Lines of curvature are important intrinsic characteristics of a curved surface used in a wide
variety of geometric analysis and processing. Although their differential attributes have been …

Closed principal lines and bifurcation Page 1 BOL. SOC. BRAS. MAT., VOL 17 N 1 (1986), 1-19
CLOSED PRINCIPAL LINES AND BIFURCATION C. Gutierrez and J. Sotomayor (1) Abstract …

Every positive C∞-quadratic differential form defined on an oriented surface has two
transverse C∞-one-dimensional foliations with common singularities associated to it. In this …

This is an essay on the historical landmarks leading to the study of principal confgurations
on surfaces in R^ 3, their structural stability and further generalizations. Here it is pointed out …