Newton-Levy-Leblond equations

ABSTRACTPhD. ThesisNEWTON-LEVY-LEBLONDEQUATIONS˙MURAT LIMONCUAnadolu UniversityGraduate School of SciencesMathematics Program˙Supervisor: Prof.Dr. Tekin DERELI2005, 70 pagesIn this thesis, it is concerned with smooth manifolds M whichcan be furnished by degenerate metric tensor. Newton-Cartan man-ifolds, Newton-Cartan connections and Galilei group are defined bythe use of co-rank one degenerate metric tensor and their propertiesare given. Orthogonal and special orthogonal group of degener-ate symmetric bilinear form, degenerate spin group are constructedby the aid of degenerate Clifford algebra, and their relation withsemi-direct product is shown. Newton-Cartan connection is liftedon degenerate spinor bundle in Newton-Cartan 4-manifold. Finally,degenerate Dirac operator and Newton-Levy-Leblond equations aredefined with the lifted connection.Keywords: Degenerate Metric Tensor, Semi-Direct Product,Degenerate Spin Group, Degenerate Spinor Bundle,Dirac Operatorii