Alexander Danilovich Alexandrov, the well-known ge-ometer, a member of the Russian Academy of Sciences and of several foreign academies, will turn 85. A. D. Alexandrov's seminal research papers cover areas ranging from quantum mechanics to geometry to philosophy of science. In particular, his innovative approach to foundations of space-time geometry is… (More)
Segal's chronometry is based on a space–time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). There are exactly two more non-commutative four-dimensional Lie algebras that admit such a form. They determine space–times L and F. The world F is based on the Lie algebra u(1,1), in… (More)
The paper deals with two simply connected solvable four-dimensional Lie groups M 1 and M 2. The first group is a direct product of the nilpotent Heisen-berg Lie group and the one-dimensional Lie group. The second one is a direct product of the two-dimensional non-abelian Lie group and the two-dimensional abelian Lie group. Applying Methods of [4, 6] we… (More)
The fractional linear action of SO(3,3) on the projective space SO(3) is proven to be a (globally defined) projective action. metrics, geodesics, 2-cover of S 1 SO(3) by Segal's compact cosmos U(2).