A Formula for Popp’s Volume in Sub-Riemannian Geometry

• Autorzy: Davide Barilari , Luca Rizzi
• Języki publikacji: EN

Abstrakty

EN

For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian distribution. As a first application of this result, we prove an explicit formula for the canonical sub- Laplacian, namely the one associated with Popp’s volume. Finally, we discuss sub-Riemannian isometries, and we prove that they preserve Popp’s volume. We also show that, under some hypotheses on the action of the isometry group of M, Popp’s volume is essentially the unique volume with such a property.

Słowa kluczowe

EN

Sub-Riemannian geometry; Popp’s volume; Sub-Laplacian; Sub-Riemannian isometries

Kategorie tematyczne

• 53C17: Sub-Riemannian geometry
• 28D05: Measure-preserving transformations

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 42-57

Daty

otrzymano

2012-11-15

zaakceptowano

2012-12-06

online

2013-01-14

Twórcy

autor

Davide Barilari

• CNRS, CMAP, École Polytechnique, Paris and Équipe INRIA
  GECO Saclay-Île-de-France, Paris, France

autor

Luca Rizzi

• SISSA, Via Bonomea 265, Trieste, Italy

Bibliografia

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Identyfikatory

DOI

10.2478/agms-2012-0004