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

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.

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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

Published: Summer 2010
First available in Project Euclid: 14 October 2011

zbMATH: 1232.53008
MathSciNet: MR2846479
Digital Object Identifier: 10.1215/ijm/1318598678

Subjects:
Primary: 53B25
Secondary: 53B35, 53C38, 58A15

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 2 • Summer 2010
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