In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the k-th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac...

In this paper, powerful coding techniques for differential space-time modulation (DSTM) over Rayleigh flat fading channels and noncoherent demodulation without channel state information at the receiver are investigated. In particular, multilevel coding (MLC), bit-interleaved coded modulation (BICM), and so-called hybrid coded modulation (HCM) are devised and compared using capacity arguments. F...

We show that in special Kähler geometry of N = 2 space-time supergravity the gauge variant part of the connection is holomorphic and flat (in a Riemannian sense). A set of differential identities (Picard-Fuchs identities) are satisfied on a holomorphic bundle. The relationship with the differential equations obeyed by the periods of the holomorphic three form of Calabi-Yau manifolds is outlined...

In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in flat homogeneous spaces of the form M ∼= (G n IRn)/G where G ⊂ GL(n, IR) is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold M so th...

How does one determine a surface which is as flat as possible, such as those created by soap film surfaces? What does it mean to be as flat as possible? In this paper we address this question from two distinct points of view, one local and one global in nature. Continuing with this theme, we put a temporal twist on the question and ask how to evolve a surface so as to flatten it as efficiently ...

We present surface temperature maps for the FK Comae-type star HD 199178 (V1794 Cygni) calculated from high resolution spectra obtained in 1994 and 1995. The spot pattern evolves, but all maps reveal a large cool spot remaining nearly at the same high latitude. The main spot is 1200 – 1600 K cooler than the mean surface temperature. The observed slightly flat bottomed absorption lines would usu...

In this paper, Hamiltonian monodromy is addressed from the point of view of geometric quantization, and various differential geometric aspects thereof are dealt with, all related to holonomies of suitable flat connections. In the case of completely integrable Hamiltonian systems with two degrees of freedom, a link is established between monodromy and (2-level) theta functions, by resorting to t...