2007/06/21 by Julien Roth · 25 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Combinatorics #Exact solutions in general relativity #Field (mathematics) #Geometric Analysis and Curvature Flows #Homogeneous #Interpretation (philosophy) #Isometry (Riemannian geometry) #Isometry group #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Pure mathematics #Space (punctuation) #Spinor #Spinor field #Tensor (intrinsic definition) #Tensor field #math.DG #msc:53C27 #msc:53C40 #msc:53C80 #msc:58C40
paper · pdf · doi:10.1016/j.geomphys.2010.03.007
published in Journal of Geometry and Physics 60(6-8), 1045-1061 (Elsevier BV) · 35 pages
arxiv created 2007/06/21 · openalex publication_date 2010/03/26 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This generalizes results by T. Friedrich for \R3 and B. Morel for \Ss3 and \HH3. The main argument is the interpretation of the energy-momentum tensor of a genralized Killing spinor as the second fondamental form up to a tensor depending on the structure of the ambient space