Illinois Journal of Mathematics

Austere submanifolds of dimension four: Examples and maximal types

Marianty Ionel and Thomas Ivey

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Austere submanifolds in Euclidean space were introduced by Harvey and Lawson in connection with their study of calibrated geometries. The algebraic possibilities for second fundamental forms of 4-dimensional austere submanifolds were classified by Bryant, into three types which we label A, B and C. In this paper, we show that type A submanifolds correspond exactly to real Kähler submanifolds, we construct new examples of such submanifolds in $\mathbb{R}^6$ and $\mathbb{R}^{10}$, and we obtain classification results on submanifolds with second fundamental forms of maximal type.

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Illinois J. Math., Volume 54, Number 2 (2010), 713-746.

First available in Project Euclid: 14 October 2011

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Zentralblatt MATH identifier

Primary: 53B25: Local submanifolds [See also 53C40]
Secondary: 53B35: Hermitian and Kählerian structures [See also 32Cxx] 53C38: Calibrations and calibrated geometries 58A15: Exterior differential systems (Cartan theory)


Ionel, Marianty; Ivey, Thomas. Austere submanifolds of dimension four: Examples and maximal types. Illinois J. Math. 54 (2010), no. 2, 713--746. doi:10.1215/ijm/1318598678.

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