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A NOTE ON FOCAL POINT COMPARISON IN RIEMANNIAN GEOMETRY
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  • Journal title : Honam Mathematical Journal
  • Volume 34, Issue 2,  2012, pp.273-278
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2012.34.2.273
 Title & Authors
A NOTE ON FOCAL POINT COMPARISON IN RIEMANNIAN GEOMETRY
Kim, Jong-Ryul;
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 Abstract
Using a comparison of the Jacobi differential equations instead of volume comparison by Itokawa in [3], the focal radius is estimated under the suitable Ricci and mean curvature conditions.
 Keywords
H-Jacobi tensor;Jacobi equation;Mean curvature;
 Language
English
 Cited by
 References
1.
Eschenburg J.-H., O'Sullivan, J.: Jacobi tensors and Ricci curvature, Math. Ann. 252 (1980), 1-26. crossref(new window)

2.
G.J. Galloway: A generalization of Myers' theorem and an application to relativistic cosmology, J. Diff. Geom. 14 (1977), 105-116.

3.
Itokawa, Y.: Distance spheres and Myers-type theorems for manifolds with lower bounds on the Ricci curvature, Illinois J. Math. 34 (1990), no. 4, 693-705.

4.
Kupeli, D. N.: On conjugate and focal points in semi-Riemannian geometry, Math. Z. 198 (1988), no. 4, 569-589. crossref(new window)

5.
Seon-Bu Kim, Jeong-Sik Kim, Eun-Ju Lee: An Estimate of Focal Points For Spacelike Hypersurfaces, Honam Math. J. 17 (1995), 29-39.

6.
O'Neill, B.: Semi-Riemannian Geometry with applications to Relativity, Pure Appl. Math., Academic Press, New York, 1983.