Subject: A question for the mailing list
From: "Boccellari" <boccellari@inwind.it>
Date: Thu, 15 Jun 2006 21:46:32 +0200

my question is not strictly for algebraic topologists, nevertheless I try 
to
submit it to your mailing list.

Let N be a smooth manifold, g and h two Riemannian structures on it, and f 
:
N ----> N a smooth.
If f is homotopic to the identity and harmonic with respect to g on the
domain and h on the codomain is it a diffeomorphism?

In dimension two and for N compact with non positive sectional curvature 
it
is true, but for higher dimension?

I will be grateful for both a direct answer and a reference.

Thank you for your kind attention.

Tommaso Boccellari