# Estimates for the Riemann Curvature Tensor

• Sergiu Klainerman
• Francesco Nicolò
Chapter
Part of the Progress in Mathematical Physics book series (PMP, volume 25)

## Abstract

This chapter is devoted to the proof of Theorem M7 in terms of the fundamental quantities Q, $$\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{Q}$$. These quantities can be expressed, according to (3.5.1), as weighted integrals of the null components of $$\hat L_0 R,\hat L_0 R,\hat L^2 _0 R,\hat L_0 \hat L_T R and \hat L_S \hat L_T R$$along the null hypersurfaces C(λ) and $$\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{C}$$(ν). We recall their explicit expressions:
$$\begin{gathered} Q(\lambda ,\nu ) = Q_1 (\lambda ,\nu ) + Q_2 (\lambda ,\nu ) \hfill \\ \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{Q} (\lambda ,\nu ) = \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{Q} _1 (\lambda ,\nu ) + \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{Q} _2 (\lambda ,\nu ) \hfill \\ \end{gathered}$$

## Keywords

Correction Term Integral Norm Riemann Curvature Tensor Null Hypersurface Connection Coefficient
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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