대한수학회지 (Journal of the Korean Mathematical Society)
- 제32권3호
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- Pages.609-614
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- 1995
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
Construction of a complete negatively curved singular riemannian foliation
- Haruo Kitahara (Department of Mathematics Kanazawa University ) ;
- Pak, Hong-Kyung (Department of Mathematics Kyungsan University )
- 발행 : 1995.08.01
초록
Let (M, g) be a complete Riemannian manifold and G be a closed (connected) subgroup of the group of isometries of M. Then the union ${\MM}$ of all principal orbits is an open dense subset of M and the quotient map ${\MM} \longrightarrow {\BB} := {\MM}/G$ becomes a Riemannian submersion for the restriction of g to ${\MM}$ which gives the quotient metric on ${\BB}$. Namely, B is a singular (complete) Riemannian space such that $\partialB$ consists of non-principal orbits.