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Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets

Abstract

We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kähler geometry.

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Correspondence to Joakim Arnlind.

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Arnlind, J., Huisken, G. Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets. Lett Math Phys 104, 1507–1521 (2014). https://doi.org/10.1007/s11005-014-0723-0

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Mathematics Subject Classification

  • 53D17
  • 53B35
  • 53B50

Keywords

  • Poisson bracket
  • Nambu bracket
  • Kähler manifold
  • Riemannian geometry
  • submanifolds
  • multi-linear brackets