Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

Die Erzeugung und Bewegung einzelner Versetzungen in Germaniumkristallen

Topographic X-ray pictures are presented showing dislocation sources in plastically deformed germanium crystals. Both internal Frank-Read sources as well as sources at the crystal surface have been observed. Dislocation velocities from 10^?6 to 10^?4 cm/sec have been evaluated.     

On the spectrum and the geometry of a spherical space form II

In this paper certain relations between the numerical coefficients of the Poisson formula of Part I and geometrical data of a spherical space form M, dim M = 2m+1 are investigated. The results yield an explicit relation between the spectrum of M and the Poincaré map of certain closed geodesics of M. Furthermore, explicit formulas for the multiplicities of the eigenvalues of the Laplacian of M are derived by means of the Poisson formula. At the end of the paper the information about M is examined which is contained in a finite part of spec(M). A partial answer is given in the Corollaries 3 and 6.     

On the spectrum and the geometry of the spherical space forms,I

In this paper we study some relations between the spectrum and the lengths of the closed geodesics of a Riemannian manifold of positive constant sectional curvature 1. Our topic is the development of a Poisson formula for such space forms. Further we obtain explicit results for the lengths of the closed geodesics. We conclude the paper with a result concerning the singular support of the distribution , where the sum runs through all spec(M).     

Macrocyclic polyfunctional lewis bases—VI: Polyoxaferrocenophanes

1,1'-Dihydroxyferrocene reacts with chloroethers 7–11 forming the respective polyoxaferrocenophanes 2–6. These compounds behave analogously to the “crown” ethers.     

Promotion of sugar-lectin recognition through the multiple sugar presentation offered by regioselectively addressable functionalized templates (RAFT): a QCM-D and SPR study

The investigation of recognition events between carbohydrates and proteins, especially the understanding of how spatial factors and binding avidity are correlated, remains a great interest for glycobiology. In this context we have investigated by nanogravimetry (QCM-D) and surface plasmon resonance (SPR), the kinetics and thermodynamics of the interaction between concanavalin A (Con A) and various neoglycopeptide ligands of low molecular weight. Regioselectively addressable functionalized templates (RAFT) have been used as scaffolds for the design of multivalent neoglycopeptides bearing thiol or biotin functions for their anchoring on transducer surfaces. Although these multivalent neoglycopeptide ligands cannot span multiple binding sites within the same Con A protein, they have increased activities relative to their monovalent counterpart. Our results emphasize that the multivalent RAFT ligands function by clustering several lectins, which leads to enhanced affinities.     

Geodesic spheres and two-point homogeneous spaces

In the Osserman conjecture and in the isoparametric conjecture it is stated that two-point homogeneous spaces may be characterized via the constancy of the eigenvalues of the Jacobi operator or the shape operator of geodesic spheres, respectively. These conjectures remain open, but in this paper we give complete positive results for similar statements about other symmetric endomorphism fields on small geodesic spheres. In addition, we derive more characteristic properties for this class of spaces by using other properties of small geodesic spheres. In particular, we study Riemannian manifolds with (curvature) homogeneous geodesic spheres. Supported by the Akademie der Naturforscher Leopoldina.