Linguistic Circle of New York

Abstract

During the academic year 1959-60 the monthly meetings of the Circle took place, as usual, between 2 and 4 p.m. on the second Saturday of each month from October through April in the auditorium of the French Consulate, 934 Fifth Avenue at 75th Street, New York City.

Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces

“…Also, they [8] found that many 1+1dimensional integrable equations like KdV, Burgers, Sawada-Kotera, Harry-Dym hierarchies and Camassa-Holm equations arise from motions of plane curves in centro-affine, similarity, affine and fully affine geometries. The motion of curves on two-dimensional surfaces in E 3 1 was considered by Gürses [18]. Therefore, the motion of Lorentzian similar (null and nonnull) curves in Lorentzian-Minkowski similarity geometries will be investigated as well.…”

“…Berger [3] represented the broad content of similarity transformations of Euclidean space. Encheva and Georgiev [12,13] studied the differential geometric invariants of curves according to a similarity in the Euclidean n-space.…”

The Geometric Invariants of Null Cartan Curves Under The Similarity Transformations

“…It can be separated to the four different cases as the following. We can take the initial conditions (17) in the example 8 for the all cases. Case 1: Let's take κγ 1 = 0 and τγ 1 = 0.…”

“…Berger [17] represented the broad content of similarity transformations in the arbitrary dimensional Euclidean spaces. Encheva and Georgiev [21,22] studied the differential geometric invariants of curves according to a similarity in the finite dimensional Euclidean spaces.…”

Some Results on p-Shape Curvatures of Non-Lightlike Space Curves

“…The broad content of similarity transformations were given by [5] in the Euclidean space. The differential geometric invariants of space curves according to the group of similarities were studied by [7] in the Euclidean 3-space.…”