Sub-Riemannian structures in a principal bundle and their Popp measures

Abstract

In this note, we explain a relation between the Popp measures of sub-Riemannian structures on the total space of a principal bundle and the base manifold. Then we determine several concrete cases explicitly.

Keywords:

• Principal bundle
• sub-Riemannian structure
• Popp measure
• divergence
• sub-Laplacian

AMS Subject Classifications:

• Primary 53C17
• 58A10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author acknowledges support through the DFG project BA 3793/6-1 in the framework of the SPP Geometry at Infinity. The second author was partially supported by the JSPS Grant-in-Aid for Scientific Research(C) [grant number 26400124]. Also the second and the third authors were partially supported by the National Center for Theoretical Science, National Taiwan University Taipei and the China Medical University, Taichung, Taiwan