This paper gives a characterization of surjective isometries on spaces of continuously differentiable functions with values in a finite-dimensional real Hilbert space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-4, author = {Fernanda Botelho and James Jamison}, title = {Surjective isometries on spaces of differentiable vector-valued functions}, journal = {Studia Mathematica}, volume = {192}, year = {2009}, pages = {39-50}, zbl = {1170.46027}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-4} }
Fernanda Botelho; James Jamison. Surjective isometries on spaces of differentiable vector-valued functions. Studia Mathematica, Tome 192 (2009) pp. 39-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-4/