This paper concerns the topology of the isospectral real manifold of the sl(N) periodic Toda lattice consisting of 2 different systems. The solutions of those systems contain blow-ups, and the set of those singular points defines a devisor of the manifold. Then adding the divisor, the manifold is compactified as the real part of the (N − 1)dimensional Jacobi variety associated with a hyperellip...

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl ...

The spectrum (of the Dirichlet Laplacian) of non-compact, non-complete Riemannian manifolds is much less understood than their compact counterparts. In particular it is often not even known whether such a manifold has any discrete spectra. In this article, we will prove that a certain type of non-compact, non-complete manifold called the quantum tube has non-empty discrete spectrum. The quantum...

Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends By Pascal Philipp We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped-product type. Our main result is an upper bound on the resonance counting function, with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base ...

• Topology of G/T : Flag manifolds G/T have cohomology only in even degrees, with Euler characteristic the degree of the Weyl group. The Euler characteristic can be calculated by a Lefschetz fixed point argument (see Adams [1], pgs. 90-92 for this). Identifying the flag manifold with a co-adjoint orbit, there is a Morse theory calulation of the cohomology that goes back to Bott, for an outline ...

The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr black holes are isosp...

We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a deformation of the classical phase-space: instead of being a vector space it becomes a manifold, the topology of which is given by the commutator relations. It ...