1967/01/01 by Philip Hartman · 316 citations
Mathematics · #Mathematics and Applications #Algebraic and Geometric Analysis #History and Theory of Mathematics #Mathematics #Harmonic #Pure mathematics #Cauchy–Riemann equations #Confusion #Riemann hypothesis #Mathematical analysis #Point (geometry) #Riemann surface #Arc (geometry) #Geometry #Physics
paper · pdf · doi:10.4153/cjm-1967-062-6
published in Canadian Journal of Mathematics 19, 673-687 (Cambridge University Press)
openalex publication_date 1967/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Let M, M′ be C ∞ Riemann manifolds such that (1.0) M is compact; (1.1) M′ is complete and its sectional curvatures are non-positive. In terms of local coordinates x = ( x 1 , … , x n ) on M and y = ( y 1 , … , y m ) on M′, let the respective Riemann elements of arc-length be and Γ i jk , Γ′ α βγ be the corresponding Christoffel symbols. When there is no danger of confusion, x (or y) will represent a point of M (or M′) or its coordinates in some local coordinate system.