Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 35 Issue 3
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- Pages.563-570
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- 1998
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
SYMPLECTICITY OF 4-DIMENSIONAL NIL-MANIFOLDS AND SCALAR CURVATURE
- Kim, Jong-Su (DEPARTMENT OF MATHEMATICS, SOGANG UNIVERSITY) ;
- Yun , Gab-Jin (DEPARTMENT OF MATHEMATICS, MYONG-JI UNIVERSITY)
- Published : 1998.08.01
Abstract
We makes an explicit description of compact 4-dimensional nilmanifolds as principal torus bundles and show that they are sysmplectic. We discuss some consequences of this and give in particular a Seibebrg-Witten-invariant proof of a Grovmov-Lawson theorem that if a compact 4-dimensional nilmanifold admits a metric of zero scalar curvature, then it is diffeomorphic to 4-tours,