Showing papers on "Ricci flow published in 1973"
TL;DR: In this paper, the Ricci rotation coefficients were used to determine the geodesic lines of force in the system of second order partial differential equations in I. The algebraic and the differential dependences among the equations have been sorted out to prove that the system is determinate.
Abstract: Investigations of static gravitational fields in paper I are continued further. Instead of the system of second order partial differential equations in I, the equivalent first order system involving the Ricci rotation coefficients is dealt with here. The algebraic and the differential dependences among the equations have been sorted out to prove that the system is determinate. Then an attempt towards classifying this system of partial differential equations has been made. Except for ``the potential equation'' which is obviously elliptic, the remaining system is hyperbolic for which the characteristic surfaces have been determined. To obtain some exact solutions the lead of Newman‐Penrose is followed in constructing the complex linear combinations of the equations. The class of static universes where ``gravitational lines of force'' are geodesics have been found. In this class one subclass is transformable to the conformastat metric and the remaining one reduces to a new metric involving the gravitational ...
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