Lines of principal curvature on canal surfaces in R³
نویسندگان
چکیده
منابع مشابه
Lines of principal curvature on canal surfaces in R3.
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R3. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated...
متن کاملGeometric mean curvature lines on surfaces immersed in R3
Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature 1’C is positive) of an oriented surface immersed in ]R3. The leaves of the foliations are the lines of geometric mean curvature, along which the normal curvature is given by B/~, which is the geometric mean curvature of the principal curvatures ki , k2 of the immersi...
متن کاملLines of Principal Curvature on Canal Surfaces in R Ronaldo Garcia, Jaume Llibre and Jorge Sotomayor
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated ...
متن کاملPrincipal Lines on Surfaces Immersed with Constant Mean Curvature
Configurations of lines of principal curvature on constant mean curvature immersed surfaces are studied. Analytical models for these configurations near general isolated umbilical points and particular types of ends are found. From the existence of transversal invariant measures for the foliations by principal lines, established here, follows that the union of recurrent lines of principal curva...
متن کاملLines of Principal Curvature near Singular End Points of Surfaces in R3 Jorge Sotomayor and Ronaldo Garcia
In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean 3−space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the work of Garcia and Sotomayor (1996), devoted to the study of principal curvature nets which are structurally stable –do not change topologically– under small p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Anais da Academia Brasileira de Ciências
سال: 2006
ISSN: 0001-3765
DOI: 10.1590/s0001-37652006000300002