15 citations · 21 across the 5 of their papers we have counts for
8 papers · 1 filter
On the geometry of holomorphic curves and complex surface
Amanda Dias Falqueto, Farid Tari
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmet…
Binary differential equations associated to congruences of lines in Euclidean 3-space
J. W. Bruce, F. Tari
We study quotients of quadratic forms and associated polar lines in the projective plane. Our results, applied pointwise to quadratic differential forms, shed some light on classic…
On the multiplicity of umbilic points
Marco Antonio do Couto Fernandes, Farid Tari
We introduce an invariant of umbilic points on surfaces in the Euclidean or Minkowski 3-space that counts the maximum number of stable umbilic points they can split up under deform…
On k-folding map-germs and hidden symmetries of surfaces in the Euclidean 3-space
G. Peñafort Sanchis, F. Tari
Let be a smooth surface in (or a complex surface in ) and be an integer. At any point on and for any plane in , we constru…
Wave maps and constant curvature surfaces: singularities and bifurcations
David Brander, Farid Tari
Wave maps (or Lorentzian-harmonic maps) from a -dimensional Lorentz space into the -sphere are associated to constant negative Gaussian curvature surfaces in Euclidean 3-sp…
Families of spherical surfaces and harmonic maps
David Brander, Farid Tari
We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifu…
On the flat geometry of the cuspidal edge
Raúl Oset Sinha, Farid Tari
We study the geometry of the cuspidal edge in derived from its contact with planes and lines (referred to as flat geometry). The contact of with planes is mea…
Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics
A. O. Remizov, F. Tari
We consider a pseudo-Riemannian metric that changes signature along a smooth curve on a surface, called the discriminant curve. The discriminant curve separates the surface locally…