caa a22 4500 469066032 CHVBK 20180323132908.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF02727202 doi (NATIONALLICENCE)springer-10.1007/BF02727202 Pawar A. Nya. Tatyasaheb Athalaye Arts and Ved. S.R. Sapre, Commerce College, 415804, Deorukh, Maharashtra, India aut Stationary tensor fields in relativistic continuum mechanics [Elektronische Daten] [A. Pawar] Summary: A tensor field in relativistic continuum mechanics is said to be stationary iff its Jaumann derivative with respect to the timelike unit flow vector vanishes. The gravitational potentials, geodesic flow are always stationary. Ifg ab is the metric tensor, then the 3-dimensional projection operatorg ab −u a u b is found to be stationary when and only when the first curvature of the streamline vanishes. The necessary and sufficient conditions for the stationary character of the 2-dimensional projection operatorg ab −u a u b +P a P b are found to beK 2+(1/2)(γ123−γ123)=0,γ124=γ123, whereP a is the unit acceleration vector field,K 2 is the second curvature or torsion andγABC are the Ricci-coefficients of rotation formed from the relativistic Serret-Frenet formulae for the stream line of a particle in the continuum. The nonstationary character of the relativistic Serret-Frenet tetrad is also established. Further it is shown thatJ u J u (g ab −u a u b )=0 iffK 1=0,γ124, whereJ u is the Jaumann transport operator. Società Italiana di Fisica, 1992 Relativistic fluid dynamics nationallicence Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/10(1992-10-01), 1173-1183 107:10<1173 1992 107 40764 https://doi.org/10.1007/BF02727202 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02727202 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pawar A. Nya. Tatyasaheb Athalaye Arts and Ved. S.R. Sapre, Commerce College, 415804, Deorukh, Maharashtra, India aut NATIONALLICENCE 773 0- Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/10(1992-10-01), 1173-1183 107:10<1173 1992 107 40764 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer