相关论文: Bifurcations of Umbilic Points and Related Princip…
In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.
In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.
We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are…
In this paper are studied the simplest patterns of axial curvature lines (along which the normal curvature vector is at a vertex of the ellipse of curvature) near a critical point of a surface mapped into R4. These critical points, where…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the…
The topological structure of the lines of principal curvature, the umbilic and partially umbilic singularities of all tridimensional ellipsoids of ${\mathbb R}^4$ is described.
This paper establishes the geometric structure of the lines of principal curvature of a hypersurface immersed in ${\mathbb R}^4$ in a neighborhood of the set $\mathcal{S}$ of its principal curvature singularities, consisting of the points…
Here are described the axiumbilic points that appear in generic one parameter families of surfaces immersed in R4. At these points the ellipse of curvature of the immersion, Little, Garcia - Sotomayor has equal axes. A review is made on the…
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…
By means of periodic orbit theory and deformed cavity model, we have investigated semiclassical origin of superdeformed shell structure and also of reflection-asymmetric deformed shapes. Systematic analysis of quantum-classical…
We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial…
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^3. By means of a…
We study the geometry of bifurcation sets of generic unfoldings of $D_4^\pm$-functions. Taking blow-ups, we show each of the bifurcation sets of $D_4^\pm$-functions admit a parametrization as a surface in $R^3$. Using this parametrization,…
Here are studied qualitative properties of the families of curves --foliations-- on a surface immersed in ${\mathbb R}^4$, along which it bends extremally in the direction of the mean normal curvature vector. Typical singularities and…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
In this work we study the affine principal lines of surfaces in 3-space. We consider the binary differential equation of the affine curvature lines and obtain the topological models of these curves near the affine umbilic points (elliptic…
We study generic two- and three-parameter unfoldings of a pair of orbits of quadratic homoclinic tangency in strongly dissipative systems. We prove that the corresponding stability windows for periodic orbits have various universal forms:…
We study the topological configurations of the lines of principal curvature, the asymptotic and characteristic curves on a cuspidal edge, in the domain of a parametrization of this surface as well as on the surface itself. Such…
Shell structure of the single-particle spectrum for reflection-asymmetric deformed cavity is investigated. Remarkable shell structure emerges for certain combinations of quadrupole and octupole deformations. Semiclassical periodic-orbit…