On the piecewise geodesic approximation of Andersson and Driver. (English) Zbl 1097.58008

Inahama, Yuzuru

Osaka J. Math. 42, No. 4, 791-806 (2005).

L. Andersson and B. Driver [J. Funct. Anal. 165, No. 2, 430–498 (1999; Zbl 0943.58024)] proved a piecewise geodesic approximation formula for path integrals on compact Riemannian manifolds. In this context geodesics are those of the Levi-Civita connection.
The author in this paper proves a generalization of the Andersson-Driver result for \(H^1\)-type metric to the case of general metric connections.
Metric connections other than the Levi-Civita connection naturally appear in stochastic analysis on Lie groups and homogeneous spaces.

Reviewer: Themistocles M. Rassias (Athens)

MSC:

58D30	Applications of manifolds of mappings to the sciences
58J65	Diffusion processes and stochastic analysis on manifolds

Keywords:

tensor; path integral; piecewise geodesic approximation; compact Riemannian manifolds; metric connections

Citations:

Zbl 0943.58024