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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Twisted calibrations


Author: Timothy A. Murdoch
Journal: Trans. Amer. Math. Soc. 328 (1991), 239-257
MSC: Primary 53C42; Secondary 58E35
MathSciNet review: 1069738
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Abstract: The methods of calibrated geometry are extended to include nonorientable submanifolds which can be oriented by some real Euclidean line bundle. Specifically, if there exists a line bundle-valued differential form of comass one which restricts to a submanifold to be a density, then the submanifold satisfies a minimizing property. The results are applied to show that the cone on the Veronese surface minimizes among a general class of comparison $ 3$-folds.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1069738-9
Article copyright: © Copyright 1991 American Mathematical Society