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Title: Clifford approach to metric manifolds (English)
Author: Chisholm, J. S. R.
Author: Farwell, R. S.
Language: English
Journal: Proceedings of the Winter School "Geometry and Physics"
Issue: 1990
Pages: [123]-133
Category: math
Summary: [For the entire collection see Zbl 0742.00067.]\par For the purpose of providing a comprehensive model for the physical world, the authors set up the notion of a Clifford manifold which, as mentioned below, admits the usual tensor structure and at the same time a spin structure. One considers the spin space generated by a Clifford algebra, namely, the vector space spanned by an orthonormal basis $\{e\sb j: j=1,\dots,n\}$ satisfying the condition $\{e\sb i,e\sb j\}\equiv e\sb ie\sb j=e\sb je\sb i=2I\eta\sb{ij}$, where $I$ denotes the unit scalar of the algebra and ($\eta\sb{ij}$) the nonsingular Minkowski metric of signature ($p,q$), ($p+q=n$). Then, for a raw manifold structure with local chart ($x\sp i$), one assigns the vector basis $\{e\sb \mu(x): \mu=1,\dots,n\}$, by the rule $e\sb \mu(x)=h\sb \mu\sp i(x)e\sb i$, $(\text{det}(h\sb \mu\sp i)\ne 0)$, so that $g\sb{\lambda\mu}(x)=h\sp i\sb{\lambda}(x)h\sp j\sb \mu(x)e\sb{ij}$ becomes a metric. A differentiable ma! (English)
MSC: 15A66
MSC: 53A50
MSC: 53B30
MSC: 53C80
idZBL: Zbl 0752.53014
idMR: MR1151897
Date available: 2009-07-13T21:26:46Z
Last updated: 2012-09-18
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