We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces. Recently, Oshima [67] published his formula for c-function for L 2 on pseudo-Riemannian symmetric spaces (see also works of Delorm [12] and van den Ban– Schlichtkrull [3], [4]). After this, there arises a natural question about other solvable problems of non-commutative harmonic analysis. In the Appendix to the paper...

In 1912 Bieberbach proved that every compact flat Riemannian manifold M is finitely covered by a flat torus. More precisely, M has the form (F\G)/H where G is a group of translations of Euclidean space, F c G is a discrete subgroup, and H is a finite group of isometries of the space of right cosets F\G. For a proof see e.g. Wolf [18]. The condition that M has a flat Riemannian metric can be sep...

We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we...

We prove that a riemannian metric on the 2-sphere or the projective plane can be C 2 approximated by a C ∞ metric whose geodesic flow has an elliptic closed geodesic. In this paper we show how to overcome a difficulty presented by Henri Poincaré in the C 2 generic case. In 1905, H. Poincaré [34, p. 259] claimed that any convex surface in R 3 should have an elliptic or degenerate non self-inters...