scholarly journals On the stability of Riemannian manifold with parallel spinors

2005 ◽  
Vol 161 (1) ◽  
pp. 151-176 ◽  
Author(s):  
Xianzhe Dai ◽  
Xiaodong Wang ◽  
Guofang Wei
Keyword(s):  
Riemannian Manifold ◽  
Parallel Spinors ◽  
The Stability

scholarly journals Stability of Riemannian manifolds with Killing spinors

2017 ◽  
Vol 28 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Changliang Wang
Keyword(s):  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Stability Result ◽  
Warped Products ◽  
Einstein Manifolds ◽  
Killing Spinors ◽  
Parallel Spinors ◽  
Unstable Manifolds ◽  
The Stability ◽  
Complete Riemannian Manifolds

Riemannian manifolds with nonzero Killing spinors are Einstein manifolds. Kröncke proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in [Stable and unstable Einstein warped products, preprint (2015), arXiv:1507.01782v1 ]. In this paper, we obtain a new proof for this stability result by using a Bochner-type formula in [X. Dai, X. Wang and G. Wei, On the stability of Riemannian manifold with parallel spinors, Invent. Math. 161(1) (2005) 151–176; M. Wang, Preserving parallel spinors under metric deformations, Indiana Univ. Math. J. 40 (1991) 815–844]. Moreover, existence of real Killing spinors is closely related to the Sasaki–Einstein structure. A regular Sasaki–Einstein manifold is essentially the total space of a certain principal [Formula: see text]-bundle over a Kähler–Einstein manifold. We prove that if the base space is a product of two Kähler–Einstein manifolds then the regular Sasaki–Einstein manifold is unstable. This provides us many new examples of unstable manifolds with real Killing spinors.

Stability and constant boundary-value problems of harmonic maps with potential

2000 ◽  
Vol 68 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Qun Chen
Keyword(s):  
Riemannian Manifold ◽  
Energy Density ◽  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
General Class ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Boundary Value ◽  
The Stability ◽  
Harmonic Maps With Potential

AbstractLet M, N be Riemannian manifolds, f: M → N a harmonic map with potential H, namely, a smooth critical point of the functional EH(f) = ∫M[e(f)−H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.

SOME RESULTS ON HARMONIC MAPS FOR FINSLER MANIFOLDS

2005 ◽  
Vol 16 (09) ◽  
pp. 1017-1031 ◽  
Author(s):  
QUN HE ◽  
YI-BING SHEN
Keyword(s):  
Riemannian Manifold ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Energy Functional ◽  
Second Variation ◽  
Finsler Manifolds ◽  
Totally Geodesic ◽  
The Stability ◽  
The Second Variation ◽  
Weitzenböck Formula

By simplifying the first and the second variation formulas of the energy functional and generalizing the Weitzenböck formula, we study the stability and the rigidity of harmonic maps between Finsler manifolds. It is proved that any nondegenerate harmonic map from a compact Einstein Riemannian manifold with nonnegative scalar curvature to a Berwald manifold with nonpositive flag curvature is totally geodesic and there is no nondegenerate stable harmonic map from a Riemannian unit sphere Sn (n > 2) to any Finsler manifold.

The stability of a connection on Hermitian vector bundles over a Riemannian manifold

2016 ◽  
Vol 09 (01) ◽  
pp. 1650001
Author(s):  
Rohollah Bakhshandeh-Chamazkoti ◽  
Mehdi Nadjafikhah
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Riemannian Manifold ◽  
Vector Bundles ◽  
Fixed Point Method ◽  
Point Method ◽  
The Stability ◽  
Rassias Stability ◽  
Hermitian Vector Bundles

In this attempt, the stability of a connection on Hermitian vector bundles over a Riemannian manifold for the generalized Jensen-type functional equation [Formula: see text] is discussed. In fact, the main purpose of this paper is to prove the generalized Hyers–Ulam–Rassias stability of connection on between Hermitian [Formula: see text] and [Formula: see text]. Also we will use the fixed point method to prove the stability of this connection for the above generalized Jensen-type functional equation.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

Effect of Improved ThO2 Particle Dispersion in Nickel on High-Temperature Strength

1970 ◽  
Vol 28 ◽  
pp. 444-445
Author(s):  
E. R. Kimmel ◽  
H. L. Anthony ◽  
W. Scheithauer
Keyword(s):  
High Temperature ◽  
Metal Matrix ◽  
Oxide Particle ◽  
Oxide Phase ◽  
Dislocation Motion ◽  
Particle Dispersion ◽  
High Temperature Strength ◽  
Strengthening Effect ◽  
Oxide Particles ◽  
The Stability

The strengthening effect at high temperature produced by a dispersed oxide phase in a metal matrix is seemingly dependent on at least two major contributors: oxide particle size and spatial distribution, and stability of the worked microstructure. These two are strongly interrelated. The stability of the microstructure is produced by polygonization of the worked structure forming low angle cell boundaries which become anchored by the dispersed oxide particles. The effect of the particles on strength is therefore twofold, in that they stabilize the worked microstructure and also hinder dislocation motion during loading.

An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

1973 ◽  
Vol 31 ◽  
pp. 486-487
Author(s):  
Mihir Parikh
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Cross Sections ◽  
Resolving Power ◽  
Peak Intensity ◽  
Molecular Film ◽  
Resolution Electron ◽  
Dissociation Cross Section ◽  
High Resolution Electron Microscope ◽  
The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

Formation and Structure of Casein Micelles in Lactating Mammary Tissue

1970 ◽  
Vol 28 ◽  
pp. 150-151
Author(s):  
Robert J. Carroll ◽  
Marvin P. Thompson ◽  
Harold M. Farrell
Keyword(s):  
Size Distribution ◽  
G Protein ◽  
Milk Proteins ◽  
Mammary Tissue ◽  
Colloidal System ◽  
Casein Micelles ◽  
The Stability

Milk is an unusually stable colloidal system; the stability of this system is due primarily to the formation of micelles by the major milk proteins, the caseins. Numerous models for the structure of casein micelles have been proposed; these models have been formulated on the basis of in vitro studies. Synthetic casein micelles (i.e., those formed by mixing the purified αsl- and k-caseins with Ca2+ in appropriate ratios) are dissimilar to those from freshly-drawn milks in (i) size distribution, (ii) ratio of Ca/P, and (iii) solvation (g. water/g. protein). Evidently, in vivo organization of the caseins into the micellar form occurs in-a manner which is not identical to the in vitro mode of formation.

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