[For the entire collection see Zbl 0742.00067.]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 $\{e_j:j=1,\cdots ,n\}$ satisfying the condition $\{e_i,e_j\}\equiv e_i{e}_j=e_j{e}_i=2I{\eta }_{ij}$, where $I$ denotes the unit scalar of the algebra and (${\eta }_{ij}$) the nonsingular Minkowski metric of signature ($p,q$), ($p+q=n$). Then, for a raw manifold structure with local chart ($x^i$), one assigns the vector basis $\{e_{\mu }\left(x\right):\mu =1,\cdots ,n\}$, by the rule $e_{\mu }\left(x\right)=h_{\mu }^i\left(x\right)e_i$, $(\text{det}\left(h_{\mu }^i\right)\ne 0)$, so that $g_{\lambda \mu }\left(x\right)=h_{\lambda }^i\left(x\right)h_{\mu }^j\left(x\right)e_{ij}$ becomes a metric. A differentiable ma!

EUDML-ID : urn:eudml:doc:219957
Mots clés:

@article{701485,
     title = {Clifford approach to metric manifolds},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1991},
     pages = {[123]-133},
     mrnumber = {MR1151897},
     zbl = {0752.53014},
     url = {http://dml.mathdoc.fr/item/701485}
}

Chisholm, J. S. R.; Farwell, R. S. Clifford approach to metric manifolds, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1991), pp. [123]-133. http://gdmltest.u-ga.fr/item/701485/