Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 41-48 |
| Seitenumfang | 8 |
| Fachzeitschrift | Calculus of Variations and Partial Differential Equations |
| Jahrgang | 10 |
| Ausgabenummer | 1 |
| Publikationsstatus | Veröffentlicht - Jan. 2000 |
| Extern publiziert | Ja |
Abstract
We prove that for n > 1 one cannot immerse S2n as a minimal Lagrangian manifold into a hyperKähler manifold. More generally we show that any minimal Lagrangian immersion of an orientable closed manifold L2n into a hyperKähler manifold H4n must have nonvanishing second Betti number β2 and that if β2 = 1, L2n is a Kähler manifold and more precisely a Kähler submanifold in H4n w.r.t. one of the complex structures on H4n. In addition we derive a result for the other Betti numbers.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Calculus of Variations and Partial Differential Equations, Jahrgang 10, Nr. 1, 01.2000, S. 41-48.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Nonexistence of minimal Lagrangian spheres in hyperKähler manifolds
AU - Smoczyk, Knut
PY - 2000/1
Y1 - 2000/1
N2 - We prove that for n > 1 one cannot immerse S2n as a minimal Lagrangian manifold into a hyperKähler manifold. More generally we show that any minimal Lagrangian immersion of an orientable closed manifold L2n into a hyperKähler manifold H4n must have nonvanishing second Betti number β2 and that if β2 = 1, L2n is a Kähler manifold and more precisely a Kähler submanifold in H4n w.r.t. one of the complex structures on H4n. In addition we derive a result for the other Betti numbers.
AB - We prove that for n > 1 one cannot immerse S2n as a minimal Lagrangian manifold into a hyperKähler manifold. More generally we show that any minimal Lagrangian immersion of an orientable closed manifold L2n into a hyperKähler manifold H4n must have nonvanishing second Betti number β2 and that if β2 = 1, L2n is a Kähler manifold and more precisely a Kähler submanifold in H4n w.r.t. one of the complex structures on H4n. In addition we derive a result for the other Betti numbers.
UR - http://www.scopus.com/inward/record.url?scp=0012943743&partnerID=8YFLogxK
U2 - 10.1007/PL00013454
DO - 10.1007/PL00013454
M3 - Article
AN - SCOPUS:0012943743
VL - 10
SP - 41
EP - 48
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
ER -