in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scatter

BMS group (and it's various generalizations) at null infinity have been studied extensively in the literature as symmetry of asymptotically flat spacetimes. The intricate relationship between soft theorems and symmetries also motivated definition such asymptotic to time-like infinity. Although vector fields that generate (generalized) algebra was defined literature, has not investigated. In thi...