2012/07/18 by Eleni-Alexandra Kontou, Ken D. Olum
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Connection (principal bundle) #Curvature #Geodesic #Geometric Analysis and Curvature Flows #Geometry #Holonomy #Linear subspace #Log-polar coordinates #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Normal coordinates #Orthogonal coordinates #Physics #Point (geometry) #Pure mathematics #Quantum mechanics #Riemann curvature tensor #Riemann hypothesis #Space (punctuation) #Subspace topology #Tangent #Tangent space #Tangent vector #Tensor (intrinsic definition) #gr-qc
paper · pdf · doi:10.1088/0264-9381/30/17/175018
9 pages, 4 figures
arxiv created 2012/07/18 · openalex publication_date 2013/08/21 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We generalize the concept of Fermi normal coordinates adapted to a geodesic to the case where the tangent space to the manifold at the base point is decomposed into a direct product of an arbitrary number of subspaces, so that we follow several geodesics in turn to find the point with given coordinates. We compute the connection and the metric as integrals of the Riemann tensor. In the case of one subspace (Riemann normal coordinates) or two subspaces, we recover some results previously found by Nesterov, using somewhat different techniques.