Deformations of calibrated submanifolds with boundary. (English) Zbl 1447.53054
Karigiannis, Spiro (ed.) et al., Lectures and surveys on \(G_2\)-manifolds and related topics. Minischool and workshop on \(G_2\)-manifolds, Fields Institute, Toronto, Canada, August 19–25, 2017. New York, NY: Springer. Fields Inst. Commun. 84, 365-382 (2020).
Summary: We review some results concerning the deformations of calibrated minimal submanifolds which occur in Riemannian manifolds with special holonomy. The calibrated submanifolds are assumed compact with a non-empty boundary which is constrained to move in a particular fixed submanifold. The results extend McLean’s deformation theory previously developed for closed compact submanifolds.
For the entire collection see [Zbl 1445.53002].
For the entire collection see [Zbl 1445.53002].
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53C10 | \(G\)-structures |
| 53C38 | Calibrations and calibrated geometries |
| 58D17 | Manifolds of metrics (especially Riemannian) |
Keywords:
normal deformations of submanifolds; Calabi-Yau manifolds; special Lagrangian submanifold; coassociative submanifolds in \(G_2\)-manifolds; Cayley submanifoldsReferences:
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