Geodesic flows on spheres and the local Riemann-Roch numbers
  We calculate the local Riemann-Roch numbers of the zero sections of $T^*S^n$ and $T^*\R P^n$, where the local Riemann-Roch numbers are defined by using the $S^1$-bundle structure on their complements associated to the geodesic flows. 
Hajime Fujita, Mikio Furuta, Takahiko Yoshida
math.SG math.DG