Ricci curvature for conjugate and focal points on GRW space-times
Bull. Korean Math. Soc. 2001 Vol. 38, No. 2, 285-292
Jeong-Sik Kim and Seon-Bu Kim
Chonnam National University, Chonnam National University
Abstract : The authors compute the Ricci curvature of the GRW space-time to obtain two conditions for the conjugate points which appear as the Timelike Convergence Condition(TCG) and the Jacobi inequality. Moreover, under such two conditions, we obtain a lower bound of the length of a unit timelike geodesic for focal points emanating from the immersed spacelike hypersurface, the graph over the fiber in the GRW space-time.
Keywords : conjugate point, focal point, Timelike Convergence Condition(TCC), Generalized Robertson-Walker(GRW) space-time
MSC numbers : 53C20, 53C50
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