Osserman manifold

In differential geometry, an Osserman manifold, named after Robert Osserman, is a Riemannian manifold in which the characteristic polynomial of the Jacobi operator of unit tangent vectors is a constant on the unit tangent bundle.[1]

The Osserman conjecture, an open problem in mathematics, asks whether every Osserman manifold is either a flat manifold or locally a rank-one symmetric space.[2][3]

  1. ^ Balázs Csikós and Márton Horváth (2011), "On the volume of the intersection of two geodesic balls", Differential Geometry and its Applications.
  2. ^ Y. Nikolayevsky (2011), "Conformally Osserman manifolds of dimension 16 and a Weyl–Schouten theorem for rank-one symmetric spaces", Annali di Matematica Pura ed Applicata.
  3. ^ "Osserman conjecture". Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Osserman_conjecture&oldid=51525