We show that for generic Riemannian metrics on a closed spin manifold of dimension three the Dirac operator has only simple eigenvalues.

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient conditions for a left-invariant connection on a Lie group to be the Levi–Civita connection of some semi-Riemannian metric on the group. As a special case, we will con...

This paper investigates the relationship between two fundamental types of objects associated with a connection on a manifold: the existence of parallel semi-Riemannian metrics and the associated holonomy group. Typically in Riemannian geometry, a metric is specified which determines a Levi-Civita connection. Here we consider the connection as more fundamental and allow for the possibility of se...

We compute the functional determinant quotient (det P h)=(det P g) for the Paneitz operator P in conformally related Riemannian metrics g; h, and discuss related positivity questions.

We obtain a bifurcation result for solutions of the Lorentz equation in a semiRiemannian manifold; such solutions are critical points of a certain strongly indefinite functionals defined in terms of the semi-Riemannian metric and the magnetic field. The flow of the Jacobi equation along each solution preserves the so-called magnetic symplectic form, and the corresponding curve in the symplectic...

‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

In this paper, the segmentation problem is formulated as a problem of segmenting a Riemannian manifold. The image domain is endowed with an anisotropic metric and its segmentation is obtained by thresholding the second eigenvector of the Laplace-Beltrami operator on the Riemannian manifold so defined. The formulation is an analytic analog of a recently proposed approach to segmentation based on...