313 research outputs found
Isophote curves on timelike surfaces in Minkowski 3-space
Isophote comprises a locus of the surface points whose normal vectors make a
constant angle with a fixed vector. In this paper, isophote curves are studied
on timelike surfaces in Minkowski 3-space E31. The axises of spacelike and
timelike isophote curves are found via their Darboux frames. Subsequently, the
relationship between isophotes and slant helices is shown on timelike surfaces.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1203.438
Pseudo-Riemannian geodesics and billiards
Many classical facts in Riemannian geometry have their pseudo-Riemannian
analogs. For instance, the spaces of space-like and time-like geodesics on a
pseudo-Riemannian manifold have natural symplectic structures (just like in the
Riemannian case), while the space of light-like geodesics has a natural contact
structure. We discuss the geometry of these structures in detail, as well as
introduce and study pseudo-Euclidean billiards. In particular, we prove
pseudo-Euclidean analogs of the Jacobi-Chasles theorems and show the
integrability of the billiard in the ellipsoid and the geodesic flow on the
ellipsoid in a pseudo-Euclidean space.Comment: title abbreviated, text edited; to appear in Advances in Mathematic
Lagrangian submanifolds in affine symplectic geometry
We uncover the lowest order differential invariants of Lagrangian
submanifolds under affine symplectic maps, and find out what happens when they
are constant.Comment: 23 pages, no figure
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