Vol.3, No 11, 2001 pp. 55-70
UDC 517.93:514.13:528.232.22(045)
CONTRIBUTION
TO THE DISCUSSION ON ABSOLUTE
INTEGRATION OF
DIFFERENTIAL EQUATIONS
OF GEODESICS
IN NON-EUCLIDEAN SPACE
Zoran Drašković
Military Technical Institute, Katanićeva 15, 11000 Belgrade, Yugoslavia
Abstract. In this paper: a) the existence
of parallel propagation operators with respect to a surface, along a curve
given on that surface, is once again pointed out; b) a closed form of these
operators, in the case of a parallel transport with respect to a spherical
surface and along its great circles, is obtained; c) the opinion that an
absolute integration of differential equations of geodesics in non-Euclidean
spaces is not possible in principle (because of the very method of introducing
the covariant differentiation in these spaces) is stated.
Key words: Absolute integral, Geodesic
lines, "Riemannian shifters".
PRILOG RASPRAVI
O APSOLUTNOM INTEGRALJENJU
DIFERENCIJALNIH
JEDNAČINA GEODEZIJSKIH LINIJA
U NEEUKLIDSKOM
PROSTORU
U radu je: a) još jednom istaknuto da postoje
operatori paralelnog pomeranja po površi duž krive zadate na toj površi;
b) dobijen je zatvoreni oblik tih operatora za slučaj paralelnog pomeranja
po sfernoj površi, a duž velikih krugova; c) iznet je stav da apsolutno
integraljenje diferencijalnih jednačina geodezijskih linija u neeuklidskim
prostorima principski nije moguće zbog samog postupka kojim je u tim prostorima
uvedeno kovarijantno diferenciranje.
