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In the previous chapter the connection operator \(\nabla \) and the metric tensor \(\mathtt {g}\) were introduced independently. In this chapter we address the question of how to uniquely fix \(\nabla \) , discuss its relevance for spacetime applications and introduce the notions of metric compatibility, isometries, Killing vectors and the Weyl tensor.

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Metric-Compatible Connections, Isometries and Killing Tensor Fields

  • 章节

  • 发表日期：

    2025年

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  • Robin W. Tucker,
  • Timothy J. Walton

摘要

In the previous chapter the connection operator \(\nabla \) and the metric tensor \(\mathtt {g}\) were introduced independently. In this chapter we address the question of how to uniquely fix \(\nabla \) , discuss its relevance for spacetime applications and introduce the notions of metric compatibility, isometries, Killing vectors and the Weyl tensor.