Circular $m$-functions
Circular $m$-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct an example of a four-dimensional manifol $dM^4$ with boundary $∂M^4$ that satisfies the condition $ξ(∂M 4) = ξ(M^4,∂M^4) = 0$ but does not contain any circularm-...
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| Datum: | 1994 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1994
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5707 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Circular $m$-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct an example of a four-dimensional manifol $dM^4$ with boundary $∂M^4$ that satisfies the condition $ξ(∂M 4) = ξ(M^4,∂M^4) = 0$ but does not contain any circularm-function. We prove that a manifold with boundary $M^n (n ≥ 5)$ such that $ξ(∂M^n , ∂M^n ) = 0$ always contains a circularm-function without critical points in the interior manifold. |
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