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Gray, A. and Vanhecke, L. (1979) Riemannian Geometry as Determined by the Volumes of Small Geodesic Balls. Acta Mathematica, 142, 157-198.
https://doi.org/10.1007/BF02395060

has been cited by the following article:

• TITLE: Bach-Einstein Gravitational Field Equations as a Perturbation of Einstein Gravitational Field Equations

  AUTHORS: Fathy Ibrahim Abdel-Bassier, Ahmed Fouad Abdel-Wahab, Fayrouz Mostafa Abdel-Maboud

  KEYWORDS: Gravitational Theory, Higher Order Gravity, Buchdahl’s Formula, Bach-Einstein Gravitational Field Equations, Raychaudhuri Equation, Tolman’s Formula

  JOURNAL NAME: Applied Mathematics, Vol.13 No.12, December 30, 2022

  ABSTRACT: The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of Einstein’s gravity. An approximate inversion formula is derived which admits a comparison of the two field theories. An application to these theories is given where the gravitational Lagrangian is expressed linearly in terms of R, R2, |Ric|2, where the Ricci tensor Ric = Rαβdxαdxβ is inserted in some formulas which are of geometrical or physical importance, such as; Raychaudhuri equation and Tolman’s formula.