Open AccessPOSSIBLE SPACE-TIME MANIFOLDS AND KINEMATICS
Author(s) -
Ln Zhang,
Zhongjun Zhou
Publication year - 1981
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.30.35
Subject(s) - kinematics , group (periodic table) , manifold (fluid mechanics) , lie group , pure mathematics , space (punctuation) , rotation (mathematics) , inertial frame of reference , physics , mathematics , geometry , mathematical analysis , classical mechanics , computer science , quantum mechanics , mechanical engineering , engineering , operating system
In this work, analysis of the space-time manifold, their kinematic groups and Lie algebras are made intuitive as far as possible. First of all, from the analysis of the iner-tial frames it is shown that according to the Beltrami theorem in Riemann Geometry, the space-time manifold, in which there exists global inertial frame, should be a pseudo-sphere. So that the kinematic group must be a rotation group, thus the explicity analy-tical expressions of such kinematical transformations and the commutative relations among the corresponding generators can be formulated easily. Consequently, the con-tractions of such manifolds, kinematic groups and Lie algebras can be deduced concretely and intuitively.