Austere Submanifolds of Dimension Four: Examples and Maximal Types

Details Austere Submanifolds of Dimension Four: Examples and Maximal Types Austere Submanifolds of Dimension Four: Examples and Maximal Types

2009-06-24

arxiv.org/abs/0906.4477v1

Mathematics

Differential Geometry

26 pages

Scientific paper

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 Kahler submanifolds, we construct new examples of such submanifolds in R^6 and R^10, and we obtain classification results on submanifolds of types B and C with maximal second fundamental forms.

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