In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimun number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space-time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is,...

The local geometric properties such as curvatures and normal vectors play important roles in analyzing the local shape of objects. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the curvatures of meshes, because there is no exact definition of the discrete curvature in meshes. In this paper, we indicate the fatal error in com...

SUMMARY Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing orientations shapes, respectively, of geological reflecting surfaces. Commonly, input data set their computation consists fine 3-D grids scalar fields representing either seismic-driven reflectivities (e.g. amplitudes migrated volumes) or mo...

We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D = 10 or D = 11 which is exactly the conditions for superstrings or M-theory. We obtain analytic solutions w...