Seminar M. Wintraecken

M. Wintraecken
JBI / Kapteyn, Groningen

 The Gauss‐Bonnet theorem relates local differen al geometrical quan es, that is quan es which depend only on the Riemannian metric and its deriva ves, by integra on to a global topological invariant, namely the Euler characteris c $  (\chi)  $. It is not directly obvious that the Euler characteris c is the only quan ty which can be established in this manner. We shall prove for a surface that if $  f  $ is a func on that can be expressed locally in terms of the metric and all its deriva ves such that $ \int_M f dA = t $ where $  t  $ is a topological invariant, then $  t = c \chi $ for some constant $ c $.

Wednesday, March 27, 2013 - 15:10 - 15:30