Abstract
In this paper we use Cliord algebra and spinor calculus to study the calibrations on Riemannian manifolds and the Grass- mann manifolds. Show that for every Grassmannian, there is a map p : Gðk; R m Þ! M such that every x A M is a calibration on R m and p � 1 ðxÞ is the contact set of x. In low dimensional cases, the cali- bration sets M are manifolds or manifolds with singularities. We also use Cliord algebra to study the isotropy groups of calibrations.
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