共查询到20条相似文献,搜索用时 15 毫秒
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A curve α immersed in the three-dimensional sphere S3 is said to be a Bertrand curve if there exists another curve β and a one-to-one correspondence between α and β such that both curves have common principal normal geodesics at corresponding points. The curves α and β are said to be a pair of Bertrand curves in S3. One of our main results is a sort of theorem for Bertrand curves in S3 which formally agrees with the classical one: “Bertrand curves in S3 correspond to curves for which there exist two constants λ≠0 and μ such that λκ+μτ=1”, where κ and τ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S3 as the only twisted curves in S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3 and (1,3)-Bertrand curves in R4. 相似文献
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This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space–time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the six-dimensional case in which twistor space is the 6-quadric Q in CP7 with a view to applications to the self-dual (0,2)-theory. We show how spinor-helicity momentum eigenstates have canonically defined distributional representatives on twistor space (a story that we extend to arbitrary dimension). These yield an elementary proof of the surjectivity of the Penrose transform. We give a direct construction of the twistor transform between the two different representations of massless fields on twistor space (H2 and H3) in which the H3s arise as obstructions to extending the H2s off Q into CP7. 相似文献
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Heavy quark effective theory predicts that produced charm quarks have the same probability to fragment into any of the four D mesons with orbital angular momentum L=0: the singlet D state and the triplet D∗ states. This would imply PV(D∗,D)=3/4, where PV is the ratio between directly produced L=0 vector states (D∗) and all L=0 (D and D∗) states. Experimental data collected in several different collision systems (e+e−, hadro-production, photo-production, etc.) and over a broad range of collision energies, show that PV(D∗,D)=0.594±0.010. From this observation, it follows that “naive spin counting” does not apply to charm production, implying a revision of charm production calculations where this assumption is made. 相似文献
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P. enczykowski 《Physics letters. [Part B]》2008,660(5):567-572
We propose that the whole algebraic structure of the Harari–Shupe rishon model originates via a Dirac-like linearization of quadratic form x2+p2, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari–Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U(1)⊗SU(3) combined with SU(2), with two of the SU(2) generators not commuting with reflections. An interpretation of intra-generation quark–lepton transformations in terms of genuine rotations and reflections in phase space is proposed. 相似文献
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The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution
Lattice artifacts in the 2d O(n) non-linear σ -model are expected to be of the form O(a2), and hence it was (when first observed) disturbing that some quantities in the O(3) model with various actions show parametrically stronger cutoff dependence, apparently O(a), up to very large correlation lengths. In a previous letter Balog et al. (2009) [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O(a2) artifacts which are especially large (ln3a) for n=3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O(3) and O(4) are also presented. 相似文献
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We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S3. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2). We show that the N -block sectors reproduce SU(N) Yang–Mills theory on S2 as the matrix size goes to infinity. 相似文献
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We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with λ≥0) in a Euclidean space EN. Assume that the immersion is proper , that is, the preimage of every compact set in EN is also compact in M. Then, we prove that M is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ<0, we construct examples of biminimal submanifolds and curves. 相似文献
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We construct examples of singular self-dual Zollfrei metrics explicitly, by patching a pair of Petean’s self-dual split-signature metrics. We prove that there is a natural one-to-one correspondence between these singular metrics and a certain set of embeddings of RP3 to CP3 which has one singular point. This embedding corresponds to an odd function on R that is rapidly decreasing and pure imaginary valued. The one-to-one correspondence is explicitly given by using the Radon transform. 相似文献
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The setting is an ergodic dynamical system (X,μ) whose points are themselves uniformly discrete point sets Λ in some space Rd and whose group action is that of translation of these point sets by the vectors of Rd. Steven Dworkin’s argument relates the diffraction of the typical point sets comprising X to the dynamical spectrum of X. In this paper we look more deeply at this relationship, particularly in the context of point processes. 相似文献
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We construct a natural L2-metric on the perturbed Seiberg–Witten moduli spaces Mμ+ of a compact 4-manifold M, and we study the resulting Riemannian geometry of Mμ+. We derive a formula which expresses the sectional curvature of Mμ+ in terms of the Green operators of the deformation complex of the Seiberg–Witten equations. In case M is simply connected, we construct a Riemannian metric on the Seiberg–Witten principal U(1) bundle P→Mμ+ such that the bundle projection becomes a Riemannian submersion. On a Kähler surface M, the L2-metric on Mμ+ coincides with the natural Kähler metric on moduli spaces of vortices. 相似文献
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For a simply connected, compact, simple Lie group G, the moduli space of flat G-bundles over a closed surface Σ is known to be pre-quantizable at integer levels. For non-simply connected G, however, integrality of the level is not sufficient for pre-quantization, and this paper determines the obstruction–namely a certain cohomology class in H3(G2;Z)–that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups G. 相似文献