Abstract
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.
Citation
Marianty Ionel. Thomas Ivey. "Austere submanifolds of dimension four: Examples and maximal types." Illinois J. Math. 54 (2) 713 - 746, Summer 2010. https://doi.org/10.1215/ijm/1318598678
Information