Clifford approach to metric manifolds

Chisholm, J. S. R., and Farwell, R. S.. "Clifford approach to metric manifolds." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1991. [123]-133. <http://eudml.org/doc/219957>.

@inProceedings{Chisholm1991,
abstract = {[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 $\lbrace e_j: j=1,\dots ,n\rbrace $ satisfying the condition $\lbrace e_i,e_j\rbrace \equiv e_ie_j=e_je_i=2I\eta _\{ij\}$, 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 $\lbrace e_\mu (x): \mu =1,\dots ,n\rbrace $, by the rule $e_\mu (x)=h_\mu ^i(x)e_i$, $(\text\{det\}(h_\mu ^i)\ne 0)$, so that $g_\{\lambda \mu \}(x)=h^i_\{\lambda \}(x)h^j_\mu (x)e_\{ij\}$ becomes a metric. A differentiable ma!},
author = {Chisholm, J. S. R., Farwell, R. S.},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics},
location = {Palermo},
pages = {[123]-133},
publisher = {Circolo Matematico di Palermo},
title = {Clifford approach to metric manifolds},
url = {http://eudml.org/doc/219957},
year = {1991},
}

TY - CLSWK
AU - Chisholm, J. S. R.
AU - Farwell, R. S.
TI - Clifford approach to metric manifolds
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1991
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [123]
EP - 133
AB - [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 $\lbrace e_j: j=1,\dots ,n\rbrace $ satisfying the condition $\lbrace e_i,e_j\rbrace \equiv e_ie_j=e_je_i=2I\eta _{ij}$, 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 $\lbrace e_\mu (x): \mu =1,\dots ,n\rbrace $, by the rule $e_\mu (x)=h_\mu ^i(x)e_i$, $(\text{det}(h_\mu ^i)\ne 0)$, so that $g_{\lambda \mu }(x)=h^i_{\lambda }(x)h^j_\mu (x)e_{ij}$ becomes a metric. A differentiable ma!
KW - Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics
UR - http://eudml.org/doc/219957
ER -