2010/11/12 by Christopher Godbout, Godbout, Christopher
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1011.3055
8 pages
openalex publication_date 2010/11/12 · arxiv created 2011/12/16 · arxiv updated 2011/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1974, S.-S. Chern and J. Simons published a paper where they defined a new type of characteristic class - one that depends not just on the topology of a manifold but also on the geometry. The goal of this paper is to investigate what kinds of geometric information is contained in these classes by studying their behavior under the Ricci flow. In particular, it is shown that the Chern- Simons class corresponding to the first Pontryagin class is invariant under the Ricci flow on the warped products S2×f S1 and S1 ×f S2 but that this class is not invariant under the Ricci flow on a generalized Berger sphere.