### Abstract

A discussion is given of the sectional curvature function on a four-dimensional Lorentz manifold and, in particular, on the space-time of Einstein's general relativity theory. Its tight relationship to the metric tensor is demonstrated and some of its geometrical and algebraic properties evaluated. The concept of a sectional curvature preserving symmetry, in the form of a certain smooth vector field, is introduced and discussed.

Original language | English |
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Pages (from-to) | 1077-1087 |

Number of pages | 10 |

Journal | International Journal of Geometric Methods in Modern Physics |

Volume | 3 |

Issue number | 5 |

Publication status | Published - 2006 |

### Keywords

- sectional curvature
- symmetries
- plane waves
- SPACE-TIME
- RIEMANNIAN CURVATURE
- CLASSIFICATION
- TENSORS

## Cite this

Hall, G. S. (2006). General Relativity and Sectional Curvature.

*International Journal of Geometric Methods in Modern Physics*,*3*(5), 1077-1087.