Details
| Original language | English |
|---|---|
| Pages (from-to) | 221-240 |
| Number of pages | 20 |
| Journal | Annals of Global Analysis and Geometry |
| Volume | 37 |
| Issue number | 3 |
| Publication status | Published - 1 Mar 2010 |
Abstract
We show that Lagrangian submanifolds in six-dimensional nearly Kähler (non-Kähler) manifolds and in twistor spaces Z4n+2 over quaternionic Kähler manifolds Q4n are minimal. Moreover, we prove that any Lagrangian submanifold L in a nearly Kähler manifold M splits into a product of two Lagrangian submanifolds for which one factor is Lagrangian in the strict nearly Kähler part of M and the other factor is Lagrangian in the Kähler part of M. Using this splitting theorem, we then describe Lagrangian submanifolds in nearly Kähler manifolds of dimensions six, eight, and ten.
Keywords
- Decomposition, Lagrangian, Minimal, Nearly Kähler, Twistor spaces
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Social Sciences(all)
- Political Science and International Relations
- Mathematics(all)
- Geometry and Topology
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In: Annals of Global Analysis and Geometry, Vol. 37, No. 3, 01.03.2010, p. 221-240.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Decomposition and minimality of lagrangian submanifolds in nearly Kähler manifolds
AU - Schäfer, Lars
AU - Smoczyk, Knut
PY - 2010/3/1
Y1 - 2010/3/1
N2 - We show that Lagrangian submanifolds in six-dimensional nearly Kähler (non-Kähler) manifolds and in twistor spaces Z4n+2 over quaternionic Kähler manifolds Q4n are minimal. Moreover, we prove that any Lagrangian submanifold L in a nearly Kähler manifold M splits into a product of two Lagrangian submanifolds for which one factor is Lagrangian in the strict nearly Kähler part of M and the other factor is Lagrangian in the Kähler part of M. Using this splitting theorem, we then describe Lagrangian submanifolds in nearly Kähler manifolds of dimensions six, eight, and ten.
AB - We show that Lagrangian submanifolds in six-dimensional nearly Kähler (non-Kähler) manifolds and in twistor spaces Z4n+2 over quaternionic Kähler manifolds Q4n are minimal. Moreover, we prove that any Lagrangian submanifold L in a nearly Kähler manifold M splits into a product of two Lagrangian submanifolds for which one factor is Lagrangian in the strict nearly Kähler part of M and the other factor is Lagrangian in the Kähler part of M. Using this splitting theorem, we then describe Lagrangian submanifolds in nearly Kähler manifolds of dimensions six, eight, and ten.
KW - Decomposition
KW - Lagrangian
KW - Minimal
KW - Nearly Kähler
KW - Twistor spaces
UR - http://www.scopus.com/inward/record.url?scp=77951206805&partnerID=8YFLogxK
U2 - 10.1007/s10455-009-9181-9
DO - 10.1007/s10455-009-9181-9
M3 - Article
AN - SCOPUS:77951206805
VL - 37
SP - 221
EP - 240
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
SN - 0232-704X
IS - 3
ER -