Abstract
In this paper we use Clifford algebra and spinor calculus to study the calibrations on Riemannian manifolds and the Grassmann manifolds. Show that for every Grassmannian, there is a map $\pi: G(k, \bm{R}^{m}) \to M$ such that every $\xi \in M$ is a calibration on $\bm{R}^{m}$ and $\pi^{-1}(\xi)$ is the contact set of $\xi$. In low dimensional cases, the calibration sets $M$ are manifolds or manifolds with singularities. We also use Clifford algebra to study the isotropy groups of calibrations.
Citation
Zhou Jianwei. "Spinors,Calibrations and Grassmannians." Tsukuba J. Math. 27 (1) 77 - 97, June 2003. https://doi.org/10.21099/tkbjm/1496164561
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