Timelike Bonnet surfaces in the Lorentzian 3-space

UDC 519.11 We generalize the criteria proposed by Z. Soyu\c{c}ok in the 3-dimensional Euclidean space to the Lorentz 3-space for the timelike surfaces. With an aid of this criterion we investigate nonisothermic timelike Bonnet surfaces and their associate surfaces. Finally, we consider the classification of helicoids proposed by Beneki, et al. We present nonisothermic timelike helicoids as examples illustrating our results. Thus, they satisfy the conditions as timelike Bonnet surfaces. In addition, we present the isothermic timelike minimal helicoids.