Austere submanifolds of dimension four: examples and maximal types

zbMath1232.53008arXiv0906.4477MaRDI QIDQ648762

Marianty Ionel, Thomas A. Ivey

Publication date: 28 November 2011

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.4477

zbMATH Keywords

method of moving framesaustere submanifoldscalibrated geometriesexterior differential equations

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local differential geometry of Hermitian and Kählerian structures (53B35) Exterior differential systems (Cartan theory) (58A15) Calibrations and calibrated geometries (53C38)

Related Items (5)

Stark hypersurfaces in complex projective space ⋮ Principal curvatures of homogeneous hypersurfaces in a Grassmann manifold \(\widetilde{\text{Gr}}_{ 3}(\text{Im}\mathbb{O})\) by the \(G_2\)-action ⋮ Ruled austere submanifolds of dimension four ⋮ Twisted-austere submanifolds in Euclidean space ⋮ Austere and arid properties for PF submanifolds in Hilbert spaces

Cites Work

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• Calibrated geometries
• Gauss parametrizations and rigidity aspects of submanifolds
• Ricci-flat metrics on the complexification of a compact rank one symmetric space
• Mirror symmetry is \(T\)-duality
• Calibrated subbundles in noncompact manifolds of special holonomy
• Some remarks on the geometry of austere manifolds
• A class of austere submanifolds

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