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1.
Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is
an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of non-negative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary
isometric to a round sphere, is necessarily a flat disc.
Received: 2 February 2002; in final form: 1 August 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (1991): 53C27, 53C40, 53C80, 58G25
The authors would like to thank Lars Andersson for helpful discussions and for bringing to our knowledge the information
regarding Remark 4. We are also grateful to the referee for pointing out that Corollary 5 and Corollary 6 are only valid when
the boundary is at least 2-dimensional.
Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967 相似文献
2.
Dias HV Diyabalanage HV Eldabaja MG Elbjeirami O Rawashdeh-Omary MA Omary MA 《Journal of the American Chemical Society》2005,127(20):7489-7501
Synthetic details, solid-state structures, and photophysical properties of a group of trimeric copper(I) complexes containing pyrazolate ligands are described. The reaction of copper(I) oxide and the fluorinated pyrazoles [3-(CF(3))Pz]H, [3-(CF(3)),5-(Me)Pz]H, and [3-(CF(3)),5-(Ph)Pz]H leads to the corresponding trinuclear copper(I) pyrazolates, {[3-(CF(3))Pz]Cu}(3), {[3-(CF(3)),5-(Me)Pz]Cu}(3), and {[3-(CF(3)),5-(Ph)Pz]Cu}(3), respectively, in high yield. The {[3,5-(i-Pr)(2)Pz]Cu}(3) compound was obtained by a reaction between [Cu(CH(3)CN)(4)][BF(4)], [3,5-(i-Pr)(2)Pz]H, and NEt(3). These compounds as well as {[3,5-(Me)(2)Pz]Cu}(3) and {[3,5-(CF(3))(2)Pz]Cu}(3) adopt trimeric structures with nine-membered Cu(3)N(6) metallacycles. There are varying degrees and types of intertrimer Cu...Cu interactions. These contacts give rise to zigzag chains in the fluorinated complexes, {[3-(CF(3))Pz]Cu}(3), {[3-(CF(3)),5-(Me)Pz]Cu}(3), {[3-(CF(3)),5-(Ph)Pz]Cu}(3), and {[3,5-(CF(3))(2)Pz]Cu}(3), whereas the nonfluorinated complexes, {[3,5-(Me)(2)Pz]Cu}(3) and {[3,5-(i-Pr)(2)Pz]Cu}(3) form dimers of trimers. Out of all the compounds examined in this study, {[3-(CF(3)),5-(Ph)Pz]Cu}(3) has the longest (3.848 Angstroms) and {[3,5-(Me)(2)Pz]Cu}(3) has the shortest (2.946 Angstroms) next-neighbor intertrimer Cu...Cu distance. The Cu...Cu separations within the trimer units do not vary significantly (typically 3.20-3.26 Angstroms). All of these trinuclear copper(I) pyrazolates show bright luminescence upon exposure to UV radiation. The luminescence bands are hugely red-shifted from the corresponding lowest-energy excitations, rather broad, and unstructured even at low temperatures, suggesting metal-centered emissions owing to intertrimer Cu...Cu interactions that are strengthened in the phosphorescent state. The {[3-(CF(3)),5-(Ph)Pz]Cu}(3) compound exhibits an additional highly structured phosphorescence with a vibronic structure corresponding to the pyrazolyl (Pz) ring. The luminescence properties of solids and solutions of the trimeric compounds in this study show fascinating trends with dramatic sensitivities to temperature, solvent, concentration, and excitation wavelengths. 相似文献
3.
Hijazi Oussama Montiel Sebastin Roldn Antonio 《Annals of Global Analysis and Geometry》2003,23(3):247-264
We give a sharp extrinsic lower bound for the first eigenvaluesof the intrinsic Dirac operator of certain hypersurfaces boundinga compact domain in a spin manifold of negative scalar curvature.Limiting-cases are characterized by the existence, on the domain,of imaginary Killing spinors. Some geometrical applications, as anAlexandrov type theorem, are given. 相似文献
4.
We get estimates on the eigenvalues of the Kählerian Dirac operator in terms of the eigenvalues of the scalar Laplace–Beltrami operator. In odd complex dimension, these estimates are sharp, in the sense that, for the first eigenvalue, they reduce to Kirchberg's inequality. 相似文献
5.
6.
Rawashdeh-Omary MA Rashdan MD Dharanipathi S Elbjeirami O Ramesh P Dias HV 《Chemical communications (Cambridge, England)》2011,47(4):1160-1162
{[3,5-(CF(3))(2)Pz]Ag}(3) (1) films exhibit selective/reversible sensing of small-organic-molecule (SAM) vapors, which readily switch-on bright-green (benzene or toluene) or bright-blue (mesitylene) luminescence that switches-off upon vapor removal. Vapors of electron-deficient SAMs or non-aromatic solvents did not attain luminescence switching and were not adsorbed. 相似文献
7.
The molybdenum and tungsten complexes W2(NtBu)4(pz)4(pzH).(C6H14)0.5 (pz = pyrazolate), M(NtBu)2(Me2pz)2(Me2pzH)2 (Me2pz = 3,5-dimethylpyrazolate), M(NtBu)2(tBu2pz)2 (tBu2pz = 3,5-di-tert-butylpyrazolate), M2(NtBu)4(Me2pz)2Cl2, W(NtBu)2(C2N3(iPr)2)2py2, M(NtBu)2-(CN4CF3)2py2, and W(NtBu)2(PhNNNPh)2 were prepared by various synthetic routes from the starting materials Mo(NtBu)2Cl2, W(NtBu)2(NHtBu)2, and W(NtBu)2Cl2py2. These new complexes were characterized by spectral and analytical methods and by X-ray crystal structure determinations. The volatilities and thermal stabilities were evaluated to determine the potential of the new complexes for use in thin film growth of metal nitride films. Mo(NtBu)2(tBu2pz)2 and W(NtBu)2(tBu2pz)2 were found to have the optimum combination of volatility and thermal stability for application in atomic layer deposition thin film growth procedures. 相似文献
8.
Journal of Solid State Electrochemistry - This work discusses the possibility of obtaining ZnO film on graphite, which can be widely used for photocatalysis, photocells, photodetectors, etc. The... 相似文献
9.
Oussama Graja Bacem Zghal Kajetan Dziedziech Fakher Chaari Adam Jablonski Tomasz Barszcz Mohamed Haddar 《Comptes Rendus Mecanique》2019,347(1):49-61
Planetary gearboxes are widely used in industrial machines. They usually work in harsh environments giving rise to damages and high maintenance costs. Condition monitoring is a key action allowing one to detect the presence of such damage ensuring healthy running conditions. The knowledge of the dynamic behavior of such a gearbox can be achieved using modeling tools as a primary step before conditioning the monitoring subject. In addition, modeling a gear set can help in the stage of design in order to optimize physical and geometric parameters of the system. Therefore, in this work, a two-dimensional lumped parameter model is adopted to build all vibration sources. The time-varying mesh stiffness is approximated as a square wave form. A novel mathematical formulation is proposed to model the amplitude modulation phenomenon due to the rotational motion of the planets around the center of the gearbox. Finally, the overall vibration signal is concluded as a summation of all vibration components influenced by the modulation function. 相似文献
10.
Shahrir Razey Sahamir Mohd Faizul Mohd Sabri Mohamand Syafie Mahmood Muhammad Akmal Bin Kamarudin Oussama Moutanabbir 《Liquid crystals》2018,45(4):522-535
The vibrational property of 2,3,6,7,10,11-hexakis(hexyloxy)triphenylene (HAT6) discotic liquid crystal (DLC) material is investigated in this research by using temperature-dependent Raman spectroscopy technique. One-dimensional (1D) charge transport mechanism in the DLC molecules is enabled in the columnar liquid crystalline (Dh) phase. The result indicates a high core-to-core correlation in the liquid crystal columnar phase, which has a ‘memory’ like effect that extends into isotropic phase at femtosecond timescale. This correlation is also confirmed through electrical conductivity measurement of DLCs, in which the electrical conductivity is enhanced in the DLC phase. DFT simulation was also carried out in order to elucidate the basic properties of HAT6 such as the band gap in the light of Raman spectra. An interesting outcome is that a freely unspecified boundary model produces in a more flexible molecule, resulting in a reduced band gap. Thus, this work provides an understanding of relationship between columnar order and electrical conductivity of HAT6 molecule, and potential strategy for design of DLCs in electronics application. 相似文献