Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 10 Issue 2
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- Pages.365-374
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- 1995
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
COMPACT MANIFOLDS WITH THE MINIMAL ENTROPY
- Yim, Jin-Whan (Department of Mathematics, Korea Advanced Institute of Science and Technology)
- Published : 1995.04.01
Abstract
On a compact manifold without conjugate points, the volume entropy can be obtained as the average mean curvature of the horospheres in the universal covering space. In the case when the volume entropy is zero, we prove that the universal covering space is diffeomorphic to a product space with a line factor. This fact can be considered as a surporting evidence for the Mane's conjecture, which claims the flatness of the mainfold.