El próximo viernes 6 de junio de 2015, a las 12:00 horas, en el aula C3A del Departamento de Matemáticas en Badajoz, la Prof. Dra. Dorothee Schueth, Humboldt-Universität zu Berlin (Alemania), impartirá la charla:

“Inaudibility of sixth order curvature invariants”.

RESUMEN: It is well-known that the spectrum on functions of a Riemannian manifold does not determine the integrals of the individual fourth order curvature invariants $\textrm{scal}^{^}2$, $|\textrm{ric}|^2$, $|R|^2$, which appear as summands in the second heat invariant $a_2$. We study the analogous question for the sixth order curvature invariants constituting $a_3$. None of them appears to be determined individually by the spectrum, which can be shown using various examples. In particular, we prove that two isospectral nilmanifolds of Heisenberg type with three-dimensional center are locally isometric if and only if they have the same value of $|\nabla R|$^2. In contrast, any pair of isospectral nilmanifolds of Heisenberg type with centers of dimension greater than three does not differ in any of the sixth order curvature invariants, in spite of local nonisometry.