대한수학회지 (Journal of the Korean Mathematical Society)

  • 제36권1호
  • /
  • Pages.125-137
  • /
  • 1999
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE ALMOST EVERYWHERE

  • 발행 : 1999.01.01
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초록

Under the condition of RicM $\geq$ -(n-1), injM $\geq$ I0, we prove the existence of an $\varepsilon$>0 such that on the region of volume $\varepsilon$>0 the curvature condition of splitting theorem can be weakened.

키워드

참고문헌

  1. J. Diff. Geom. v.35 $C^α$-compactness for manifolds with Ricci curvature and injectivity radius boundary below M. Anderson;J. Cheeger
  2. Ann. Global Anal. and Geom. v.11 A splitting theorem for manifolds of almost nonnegative Ricci curvature M. Cai
  3. J. Diff. Geom. v.6 The splitting theorem for manifolds of nonnegative Ricci curvature J. Cheeger;D. Gromoll
  4. Duke Math. J. v.76 Negative Ricci curvature adn isometry group X. Dai;Z. Shen;G. Wei
  5. Riemannian geometry S. Gallot;D. Hullin;J. Lafontain
  6. Kyushu J. Math. v.50 A sphere theorem under a curvature perturbation S.-H. Paeng
  7. Proc. Amer. Math. Soc. v.125 Topological entropy for geodesic flows under a Ricci curvature condition S.-H. Paeng
  8. Kyushu J. Math. v.52 A sphere theorem under a curvature perturbature Ⅱ S.-H. Paeng
  9. Lectures on Differential Geometry R. Schoen;S. -T. Yau
  10. Indiana Univ. Math. J. v.40 On Riemannian manifolds of almost nonnegative curvature Z. Shen;G. Wei