Fields on symmetric surfaces

Daniele Panozzo, Yaron Lipman, Enrico Puppo, Denis Zorin
2012 ACM Transactions on Graphics  
Appendix: Proofs of statements Proof of Proposition 2. First, consider a stationary point p of g. As shown [Montgomery and Zippin 1955] , there is a neighborhood U of p and a choice of smooth coordinates h : U → R 2 system on U such that g in these coordinates is a linear transformation is the differential of the transformation h at point p. As Dg(p) 2 = I at a stationary point, it follows that (A p g ) 2 = I. All such matrices have two eigenvalues, and both its eigenvalues satisfy λ 2 = 1.
doi:10.1145/2185520.2185607 fatcat:mok7otmqpbayldearoli3nv2oa