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2-Ruled Calibrated 4-folds in R^7 and R^8

Abstract:

In this paper we introduce the area of 2-ruled 4-folds in R^n (n=7 or 8), that is, submanifolds M of R^n that admit a fibration over some 2-fold Sigma such that each fibre is an affine 2-plane in R^n. This is motivated by the paper math.DG/0012060 by Joyce on ruled special Lagrangian 3-folds in C^3 and the work of the author in math.DG/0401123 on ruled associative 3-folds in R^7. We say that a 2-ruled 4-fold M is r-framed if we are given an oriented basis for each fibre in a smooth manner, an...

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Publication status:
Published

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Publisher copy:
10.1112/S0024610706023313

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
Journal of the London Mathematical Society (2) 74 (2006), 219-243
Volume:
74
Issue:
1
Pages:
219-243
Publication date:
2004-01-13
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
URN:
uuid:3fb8c27c-eeca-432e-8f89-383bfa4ba066
Source identifiers:
30678
Local pid:
pubs:30678
Language:
English
Keywords:

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