1978/12/01 by Vernon D. Sandberg · 1 citation
Engineering · Mathematics · #Algebraic and Geometric Analysis #Cartesian tensor #Composite Material Mechanics #Eigenfunction #Eigenvalues and eigenvectors #Elasticity and Material Modeling #Exact solutions in general relativity #Geometry #Harmonics #Laplace operator #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Solid harmonics #Spherical harmonics #Spin-weighted spherical harmonics #Tensor (intrinsic definition) #Tensor contraction #Tensor density #Tensor field #Tensor operator #Vector spherical harmonics #Zonal spherical harmonics
paper · pdf · doi:10.1063/1.523649
openalex publication_date 1978/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21
Tensor spherical harmonics for the 2-sphere and 3-sphere are discussed as eigenfunction problems of the Laplace operators on these manifolds. The scalar, vector, and second-rank tensor harmonics are given explicitly in terms of known functions and their properties summarized.