Geodesic
Spinorial matter and general relativity theory
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 35 (2010) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

World spinors, the spinorial matter (particles, $p$-branes and fields) in a generic curved space is considered. Representation theory, as well as the basic algebraic and topological properties of relevant symmetry groups are presented. Relations between spinorial wave equations that transform respectively w.r.t. the tangent flat-space (anholonomic) Affine symmetry group and the world generic-curved-space (holonomic) group of Diffeomorphisms are presented. World spinor equations and certain basic constraints that yield a viable physical theory are discussed. A geometric construction based on an infinite-component generalization of the frame fields (e.g. tetrads) is outlined. The world spinor field equation in $3D$ is treated in more details. 
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     author = {Dj. \v{S}ija\v{c}ki},
     title = {Spinorial matter and general relativity theory},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {97 - 112},
     publisher = {mathdoc},
     volume = {35},
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}
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Dj. Šijački. Spinorial matter and general relativity theory. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 35 (2010) no. 1. http://geodesic.mathdoc.fr/item/BASS_2010_35_1_a6/