Twisted Calibrations
- 1 November 1991
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 328 (1) , 239-257
- https://doi.org/10.2307/2001882
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.Keywords
This publication has 4 references indexed in Scilit:
- Area-Minimizing Surfaces, Faces of Grassmannians, and CalibrationsThe American Mathematical Monthly, 1988
- Manifolds, Tensor Analysis, and ApplicationsPublished by Springer Nature ,1988
- The exterior algebra ΛkRn and area minimizationLinear Algebra and its Applications, 1985
- Calibrated geometriesActa Mathematica, 1982