Details
| Original language | English |
|---|---|
| Pages (from-to) | 111-125 |
| Number of pages | 15 |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 41 |
| Issue number | 1-2 |
| Publication status | Published - 1 May 2011 |
Abstract
Given an almost para-Kähler manifold equipped with a metric and para-complex connection, we define a generalized second fundamental form and generalized mean curvature vector of space-like Lagrangian submanifolds. We then show that the deformation induced by this variant of the mean curvature vector field preserves the Lagrangian condition, if the connection satisfies also some Einstein condition. In case the almost para-Kähler structure is integrable, the flow coincides with the classical mean curvature flow in the pseudo-Riemannian context.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Calculus of Variations and Partial Differential Equations, Vol. 41, No. 1-2, 01.05.2011, p. 111-125.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mean curvature flow of space-like Lagrangian submanifolds in almost para-Kähler manifolds
AU - Chursin, Mykhaylo
AU - Schäfer, Lars
AU - Smoczyk, Knut
PY - 2011/5/1
Y1 - 2011/5/1
N2 - Given an almost para-Kähler manifold equipped with a metric and para-complex connection, we define a generalized second fundamental form and generalized mean curvature vector of space-like Lagrangian submanifolds. We then show that the deformation induced by this variant of the mean curvature vector field preserves the Lagrangian condition, if the connection satisfies also some Einstein condition. In case the almost para-Kähler structure is integrable, the flow coincides with the classical mean curvature flow in the pseudo-Riemannian context.
AB - Given an almost para-Kähler manifold equipped with a metric and para-complex connection, we define a generalized second fundamental form and generalized mean curvature vector of space-like Lagrangian submanifolds. We then show that the deformation induced by this variant of the mean curvature vector field preserves the Lagrangian condition, if the connection satisfies also some Einstein condition. In case the almost para-Kähler structure is integrable, the flow coincides with the classical mean curvature flow in the pseudo-Riemannian context.
UR - http://www.scopus.com/inward/record.url?scp=79952984933&partnerID=8YFLogxK
U2 - 10.1007/s00526-010-0355-x
DO - 10.1007/s00526-010-0355-x
M3 - Article
AN - SCOPUS:79952984933
VL - 41
SP - 111
EP - 125
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1-2
ER -