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]
References
edit- ^ Balázs Csikós and Márton Horváth (2011), "On the volume of the intersection of two geodesic balls", Differential Geometry and its Applications.
- ^ 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.
- ^ "Osserman conjecture". Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Osserman_conjecture&oldid=51525
External link
edit- Y. Nikolayevsky, "Two theorems on Osserman manifolds" doi.org/10.1016/S0926-2245(02)00160-2
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