Logo del repository
  1. Home
 
Opzioni

A formula for popp's volume in sub-riemannian geometry

Barilari, Davide
•
Rizzi, Luca
2013
  • journal article

Periodico
ANALYSIS AND GEOMETRY IN METRIC SPACES
Abstract
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.
DOI
10.2478/agms-2012-0004
Archivio
http://hdl.handle.net/20.500.11767/128678
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85017315214
https://arxiv.org/abs/1211.2325
Diritti
metadata only access
Soggetti
  • Popp's volume

  • Sub-laplacian

  • Sub-riemannian geomet...

  • Sub-riemannian isomet...

  • Settore MAT/05 - Anal...

google-scholar
Get Involved!
  • Source Code
  • Documentation
  • Slack Channel
Make it your own

DSpace-CRIS can be extensively configured to meet your needs. Decide which information need to be collected and available with fine-grained security. Start updating the theme to match your nstitution's web identity.

Need professional help?

The original creators of DSpace-CRIS at 4Science can take your project to the next level, get in touch!

Realizzato con Software DSpace-CRIS - Estensione mantenuta e ottimizzata da 4Science

  • Impostazioni dei cookie
  • Informativa sulla privacy
  • Accordo con l'utente finale
  • Invia il tuo Feedback