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]

References

^ 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

Y. Nikolayevsky, "Two theorems on Osserman manifolds" doi.org/10.1016/S0926-2245(02)00160-2

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[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

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