대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제37권3호
  • /
  • Pages.587-599
  • /
  • 2000
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

TOPOLOGICAL PROPERTIES OF SOME COHOMOGENEITY ONE RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

  • Mirzaie, R. (School of Science, Tarbiat Modarres University) ;
  • Kashani, S.M.B. (School of Science, Tarbiat Modarres University)
  • 발행 : 2000.08.01
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초록

In this paper we study some nonpositively curved Riemannian manifolds acted on by a Lie group of isometries with principal orbits of codimension one. Among other results it is proved that if the universal covering manifold satisfies some conditions then every nonexceptional singular orbit is a totally geodesic submanifold. When M is flat and is not toruslike, it is proved that either each orbit is isometric to $R^k\timesT^m$or there is a singular orbit. If the singular orbit is unique and nonexceptional, then it is isometric to $R^k\timesT^m$.

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참고문헌

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