The metrics of gravitational and cosmological models are brought into canonical form in comoving coordinates. The FWR curvature parameter k is read from this and it is shown that k=0 does not correlate to a flat model...The metrics of gravitational and cosmological models are brought into canonical form in comoving coordinates. The FWR curvature parameter k is read from this and it is shown that k=0 does not correlate to a flat model, but for a spatially positively curved geometry in which reference systems which are in free fall exist. This also corresponds to Einstein’s elevator principle. Moreover, we will show that our subluminal cosmos is associated with the R<sub>h</sub>=ct model of Melia, assuming that k=0 is related to a free-falling system in the sense described above.展开更多
An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under th...An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.展开更多
文摘The metrics of gravitational and cosmological models are brought into canonical form in comoving coordinates. The FWR curvature parameter k is read from this and it is shown that k=0 does not correlate to a flat model, but for a spatially positively curved geometry in which reference systems which are in free fall exist. This also corresponds to Einstein’s elevator principle. Moreover, we will show that our subluminal cosmos is associated with the R<sub>h</sub>=ct model of Melia, assuming that k=0 is related to a free-falling system in the sense described above.
基金Supported by National Natural Science Foundation of China (Grant No.10671181)
文摘An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.
