Calibrated Geometry
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form (for some 0 p n) which is a calibration in the sense that is closed: d = 0, where d is the exterior derivative for any x M and any oriented p-dimensional subspace of TxM, = vol with 1. Here vol is the volume form of with respect to g. Set Gx( ) = { as above : = vol }. (In order for the theory to be nontrivial, we…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form (for some 0 p n) which is a calibration in the sense that is closed: d = 0, where d is the exterior derivative for any x M and any oriented p-dimensional subspace of TxM, = vol with 1. Here vol is the volume form of with respect to g. Set Gx( ) = { as above : = vol }. (In order for the theory to be nontrivial, we need Gx( ) to be nonempty.) Let G( ) be the union of Gx( ) for x in M. The theory of calibrations is due to R. Harvey and B. Lawson and others (see The History of Calibrations).