Article

 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" Volume: Issue: 1990 Year: 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 Stable URL: http://hdl.handle.net/10338.dmlcz/701485 .

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