Osserman type problems in Riemannian and psuedo-Riemannian geometry

Host Institution:

La Trobe University

Title of Seminar:

Osserman type problems in Riemannian and psuedo-Riemannian geometry

Speaker's Name:

Professor Zoran Rakić

Speaker's Institution:

University of Belgrade, Serbia

Time and Date:

Thursday 24th November, 2011, 12:00 PM (AEDT)

Seminar Abstract:

Let (M, g) be a Riemannian manifold, with curvature tensor R. The Jacobi operator RX is the symmetric endomorphism of TpM defined by RX(Y) = R(Y;X)X. If M is locally a rank-one symmetric space or if M is flat, then the local isometry group acts transitively on the unit sphere bundle SM and hence the eigenvalues of RX are constant on SM. Osserman in the late eighties, wondered if the converse is true; this question is usually known as the Osserman conjecture. In the last twenty years many authors have been studied problems which arising from the Osserman conjecture and its generalizations. In the present lecture we will give an overview of Osserman type problems in Riemannian and pseudo-Riemannian geometry.

Seminar Convenor:

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AGR IT support:

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