Comparison of the NMR enantiodifferentiation of a chiral ruthenium(II) complex of C2 symmetry using the TRISPHAT anion and a lanthanide shift reagent

The tris[tetrachlorobenzenediolato]phosphate(v) anion (TRISPHAT) is known to be an efficient NMR chiral shift agent for various chiral cationic species. Here we compare the efficiency of TRISPHAT and of a chiral lanthanide shift reagent for the determination of the enantiomeric purity of the chiral building block [Ru(phen)[2]PY[2]][2][+] which possesses C[2] symmetry. We also discuss our results in terms of the geometry of interaction between the Ru(II) complex and the TRISPHAT anion.

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.