We reconstruct the Cartan frame of a null curve in Minkowski spacetime for an arbitrary parameter, and we characterize pseudo-spherical null curves and Bertrand null curves. (2000). 53B30, 53A04.
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The transformation of a system from one state to another is often mediated by a bottleneck in the system's phase space. In chemistry, these bottlenecks are known as transition states through which the system has to pass in order to evolve from reactants to products. The chemical reactions are usually associated with configurational changes where the reactants and products states correspond, e.g., to two different isomers or the undissociated and dissociated state of a molecule or cluster. In this Letter, we report on a new type of bottleneck which mediates kinetic rather than configurational changes. The phase space structures associated with such kinetic transition states and their dynamical implications are discussed for the rotational vibrational motion of a triatomic molecule. An outline of more general related phase space structures with important dynamical implications is given.
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