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1.
If M is an isoparametric hypersurface in a sphere S
n
with four distinct principal curvatures, then the principal curvatures κ1, . . . , κ4 can be ordered so that their multiplicities satisfy m
1 = m
2 and m
3 = m
4, and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible connected proper Dupin hypersurface in R
n
(or S
n
) with four distinct principal curvatures with multiplicities m
1 = m
2 ≥ 1 and m
3 = m
4 = 1, and constant Lie curvature r = −1, then M is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the
assumption of irreducibility is replaced by compactness and r is merely assumed to be constant.
相似文献
2.
Thomas E. Cecil 《Geometriae Dedicata》1989,32(3):281-300
Pinkall's standard constructions for obtaining a Dupin hypersurface W in
N
from a Dupin hypersurface M in
n
, N>n, are studied in the context of Lie sphere geometry. It is shown that a compact Dupin hypersurface W in
N
with g distinct principal curvatures at each point is reducible to a compact Dupin hypersurface M in
n
if and only if g=2.This research was supported by NSF Grant No. DMS 87-06015. 相似文献
3.
4.
5.
6.
7.
Gehan M. El-Subruiti Kamal H. Halawani Cecil F. Wells Ibrahim M. Sidahmed 《Transition Metal Chemistry》1993,18(3):323-328
Summary The kinetics of the solvolysis of complex ions trans-[Co(Rpy)4Cl2]+, with R = 4-t-Bu, 3-Me and 3-Et, have been investigated in mixtures formed by adding urea to water, which enhances the dielectric constant and decreases solvent structure. Differential effects of the changes in solvent structure on the initial and transition states are found to be important factors controlling changes in the rate constant with solvent composition. The variation of the enthalpy and the entropy of activation with solvent composition are contrasted with their variations found for the solvolysis of [Co(Rpy)4Cl2]+ in mixtures where solvent structure is enhanced by additions of a co-solvent to water. The application of a free energy cycle to the process of the initial state going to the transition state suggests that the Co3+ cation in the transition state is more stable than the Co3+ cation in the initial state in the water + urea mixtures. 相似文献
8.
Summary The kinetics of the solvolysis of thetrans-[Coen2Cl2]+ cation (en = 1,2-diaminoethane) have been investigated over a range of temperatures in water with added ethanonitrile which has much less effect on the solvent structure than the acohols already used as co-solvents with water for this solvolysis. However, the non-linear relationship obtained for the variation of log (rate constant) with the reciprocal of the dielectric constant at constant temperature shows that the effect of changing solvent structure is still important, although, as expected from the absence of pronounced extrema in the variation with composition in water + ethanonitrile of physical properties which are influenced by such changes in solvent structure, the enthalpy and entropy of activation for the solvolysis vary smoothly with composition. The application of a free energy cycle shows that changes in solvent structure affect the pentacoordinated cobalt(III) ion in the transition state more than the hexacoordinated cobalt(III) ion in the initial state. 相似文献
9.
Peter Brown Cecil L. Hornbeck John R. Cronin 《Journal of mass spectrometry : JMS》1972,6(12):1383-1399
The positive ion electron-impact mass spectra of a series of alloxazines, iso-alloxazines and some derivatives have been examined. The compounds employed were lumichrome (7,8-dimethylalloxazine), 1,3-dimethyllumichrome, lumiflavin (7,8,10-trimethyl-iso-alloxazine), 3-methyllumiflavin, riboflavin [7,8-dimethyl-10-(D-1′-ribityl)-iso-alloxazine], riboflavin tetraacetate, 3-methylriboflavin tetraacetate and riboflavin tetrapropionate. By using exact mass measurements, metastable ion defocusing and the mass/composition shifts occurring with derivatives, it has been possible to arrive at detailed interpretations of the mass spectra of all compounds. With lumichrome and lumiflavin, fragmentation commences by elimination of HNCO from the pyrimidine ring. With riboflavin and its derivatives the ribityl chain cleaves off first, followed by decomposition of the iso-alloxazine ring. Application of these methods and findings to the structural analysis of chemically interesting modified flavins is predicted to be rewarding. 相似文献
10.
L. R. G. Valadon Mohamed Osman Rosemary S. Mummery 《Photochemistry and photobiology》1979,29(3):605-607
Abstract— Ten minutes of red irradiation (R) increased carotenogenesis in Verticillium agoricinum and this effect was reversed by 10min of far-red (FR) irradiation indicating that phytochrome is involved. A far-red minus red difference spectrum of a crude extract shows a peak at 670 nm and a dip at 750 nm wavelength, values slightly larger than higher plant phytochrome. indicating the presence of phytochrome. 相似文献