General Relativity and Gravitation

, Volume 5, Issue 5, pp 555–572 | Cite as

Space tensors in general relativity I: Spatial tensor algebra and analysis

  • Enrico Massa
Research Articles


A pair (M, Γ) is defined as a Riemannian manifold M of normal hyperbolic type carrying a distinguished time-like congruence Γ. The spatial tensor algebraD associated with the pair (M, Γ) is discussed. A general definition of the concept of spatial tensor analysis over (M, Γ) is then proposed. Basically, this includes a spatial covariant differentiation\(\tilde \nabla \) and a time-derivative\(\tilde \nabla _T \), both acting onD and commuting with the process of raising and lowering the tensor indices. The torsion tensor fields of the pair\(\left( {\tilde \nabla ,\tilde \nabla _T } \right)\) are discussed, as well as the corresponding structural equations. The existence of a distinguished spatial tensor analysis over (M, Γ) is finally established, and the resulting mathematical structure is examined in detail.


Riemannian Manifold Fundamental Form Differential Form Tensor Field Natural Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Publishing Company Limited 1974

Authors and Affiliations

  • Enrico Massa
    • 1
  1. 1.Istituto Matematico dell'Università di GenovaGenovaItaly

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