Analogues of Rossi's map and E. Cartan's classification of homogeneous strongly pseudoconvex 3-dimensional hypersurfaces
We introduce analogues of a map due to Rossi and show how they can be used to explicitly determine all covers of certain homogeneous strongly pseudoconvex 3-dimensional hypersurfaces that appear in the classification obtained by E. Cartan in 1932.
Effective actions of SU_n on complex n-dimensional manifolds
We are interested in the classification all connected complex manifolds M of dimension n ≥ 2 admitting effective actions of the special unitary group SUn by biholomorphic transformations. For the full unitary group Un such a classification was obtained in [IKruzh]. One motivation for our study there was the following characterization of the complex space C obtained as a result of the classification. Let M be a connected complex manifold of dimension n and assume that the group Aut(M) of all holomorphic automorphisms of M equipped with the compact open topology is isomorphic to Aut(C) as a topological group, then M is biholomorphically equivalent to C. In fact, the above characterization holds if Aut(M) merely contains a subgroup isomorphic to the group of affine isometries of Aut(C). It appears, however, to be of independent interest to determine all ‘rotationally symmetric’ complex manifolds. From this point of view it is more natural to consider SUn-actions rather than Un-actions. On the other hand the existence of a 1-dimensional center in Un was of considerable help in [IKruzh]. The center of SUn is discrete and dimSUn = n 2 − 1. Due to this, our arguments in the case of SUn are more complicated than for Un. By an argument similar to that in [IKruzh] we find all dimensions that orbits of an SUn-action on M can a priori have. It turns out (see Proposition 1.1) that an orbit can be a point (and therefore SUn has a fixed point in M), a real hypersurface in M , a complex hypersurface in M , or the whole of M (in which case M is homogeneous).
L-band 3D imaging of an Alpine Glacier: Results from the AlpTomoSAR campaign
In this paper we present results from the tomographic analysis of L-Band SAR data acquired in February/March 2014 over the Mittelbergferner glacier, Austrian Alps, during the ESA campaign AlpTomoSAR. The campaign includes coincident in-situ measurements of snow and ice properties, as well as high-frequency Ground Penetrating Radar (GPR) data acquired over a total length of 18 km. The analyses of three-dimensional TomoSAR data cubes shows the complexity of the glacier sub-surface scattering. Most areas are characterized by surface scattering in proximity of the Lidar surface, plus a complex pattern of in-depth volumetric scattering beneath. Various subsurface features observed in GPR transects at 600 MHz and 200 MHz clearly showed up in TomoSAR sections as well. In particular: firn bodies, crevasses, and even the bedrock down to 50 m below the ice surface.