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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Product of harmonic maps is harmonic: a stochastic approach

Author(s):
Catuogno, Pedro J. ; Ruffino, Paulo R. C.
Total Authors: 2
Document type: Journal article
Source: Lecture Notes in Mathematics; v. 1899, p. 227-233, 2007.
Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics
Abstract

Let phi(j) : M(j) -> G, j = 1, 2, ... , n, be harmonic mappings from Riemannian manifolds M(j) to a Lie group G. Then the product phi(1)phi(2) ... phi(n) is a harmonic mapping between M(1) x M(2) x ... x M(n) and G. The proof is a combination of properties of Brownian motion in manifolds and Ito formulae for stochastic exponential and logarithm of product of semimartingales in Lie groups. (AU)