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Vanishing theorems in affine, Riemannian, and Lorentz geometries

Abstract

In this survey, we consider one aspect of the Bochner technique, the proof of vanishing theorems by using the Weitzenbock integral formulas, which allows us to extend the technique to pseudo-Riemannian manifolds and equiaffine connection manifolds.

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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.

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Stepanov, S.E. Vanishing theorems in affine, Riemannian, and Lorentz geometries. J Math Sci 141, 929 (2007). https://doi.org/10.1007/s10958-007-0024-6

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Keywords

  • Manifold
  • Riemannian Manifold
  • Lorentz Manifold
  • Conformal Killing
  • Conformal Killing Vector