Twisted calibrations

Murdoch, Timothy A.

doi:10.1090/S0002-9947-1991-1069738-9

Twisted calibrations
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by Timothy A. Murdoch

Trans. Amer. Math. Soc. 328 (1991), 239-257

DOI: https://doi.org/10.1090/S0002-9947-1991-1069738-9

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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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