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Geometrical characterizations are given for the tensor R⋅SRS, where SS is the Ricci tensor   of a (semi-)Riemannian manifold (M,g)(M,g) and RR denotes the curvature operator   acting on SS as a derivation, and of the Ricci Tachibana tensor  g⋅SgS, where the natural metrical operator  gg also acts as a derivation on SS. As a combination, the Ricci curvatures   associated with directions on MM, of which the isotropy determines that MM is Einstein, are extended to the Ricci curvatures of Deszcz   associated with directions and planes on MM, and of which the isotropy determines that MM is Ricci pseudo-symmetric in the sense of Deszcz.  相似文献   

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Let MM be a symplectic symmetric space, and let ?:M→V?:MV be an extrinsic symplectic symmetric immersion in the sense of Krantz and Schwachhöfer (2010) [7], i.e., (V,Ω)(V,Ω) is a symplectic vector space and ?? is an injective symplectic immersion such that for each point p∈MpM, the geodesic symmetry in pp is compatible with the reflection in the affine normal space at ?(p)?(p).  相似文献   

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An essential point of a conformal vector field ξξ on a conformal manifold (M,c)(M,c) is a point around which the local flow of ξξ preserves no metric in the conformal class cc. It is well-known that a conformal vector field vanishes at each essential point. In this note we show that essential points are isolated. This is a generalization to higher dimensions of the fact that the zeros of a holomorphic function are isolated. As an application, we show that every connected component of the zero set of a conformal vector field is totally umbilical.  相似文献   

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A complex symplectic structure on a Lie algebra hh is an integrable complex structure JJ with a closed non-degenerate (2,0)(2,0)-form. It is determined by JJ and the real part ΩΩ of the (2,0)(2,0)-form. Suppose that hh is a semi-direct product g?Vg?V, and both gg and VV are Lagrangian with respect to ΩΩ and totally real with respect to JJ. This note shows that g?Vg?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of ΩΩ and JJ are isomorphic.  相似文献   

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Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0T=0 1D insulator the charge stiffness D(T)D(T) vanishes for T>0T>0 and finite values of the on-site repulsion UU in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite TT and U>0U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0U=0 and vanishes for U>0U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0U=Uc=0 for all finite temperatures T>0T>0. (At T=0T=0 such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the ηη-spin SU(2)SU(2) symmetry with the hidden U(1)U(1) symmetry beyond SO(4)SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.  相似文献   

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Let E→MEM be a holomorphic vector bundle over a compact Kähler manifold (M,ω)(M,ω). We prove that if EE admits a ωω-balanced metric (in X. Wang’s terminology (Wang, 2005 [3])) then it is unique. This result together with Biliotti and Ghigi (2008) [14] implies the existence and uniqueness of ωω-balanced metrics of certain direct sums of irreducible homogeneous vector bundles over rational homogeneous varieties. We finally apply our result to show the rigidity of ωω-balanced Kähler maps into Grassmannians.  相似文献   

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For every diffeomorphism φ:M→Nφ:MN between 3-dimensional Riemannian manifolds MM and NN, there are locally two 2-dimensional distributions D±D± such that φφ is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of D±D±. These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator induced from φφ. We investigate the integrability condition of D+D+ and DD. We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves.  相似文献   

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Given a special Kähler manifold MM, we give a new, direct proof of the relationship between the quaternionic structure on TMTM and the variation of Hodge structures on TCMTCM.  相似文献   

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The random-crystal field spin-1 Blume–Capel model is investigated by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The crystal field is either turned on randomly with probability pp or turned off with q=1−pq=1p in a bimodal distribution. Then the phase diagrams are constructed on the crystal field (ΔΔ)–temperature (kT/J)(kT/J) planes for given values of pp and on the (kT/J,pkT/J,p) planes for given ΔΔ by studying the thermal variations of the order parameters. In the latter, we only present the second-order phase transition lines, because of the existence of irregular wiggly phase transitions which are not good enough to construct lines. In addition to these phase transitions, the model also yields tricritical points for all values of pp and the reentrant behavior at lower pp values.  相似文献   

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In this paper we study the critical behavior of the two-dimensional antiferromagnetic Ising model in both uniform longitudinal (HH) and transverse (ΩΩ) magnetic fields. Using the effective-field theory (EFT) with correlation in single site clusters we calculate the phase diagrams in the H−THT and Ω−TΩT planes for the square lattice. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.  相似文献   

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We consider a complete nonnegative biminimal   submanifold MM (that is, a complete biminimal submanifold with λ≥0λ0) in a Euclidean space ENEN. Assume that the immersion is proper  , that is, the preimage of every compact set in ENEN is also compact in MM. Then, we prove that MM is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ<0λ<0, we construct examples of biminimal submanifolds and curves.  相似文献   

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Let MM be a connected complex projective manifold such that c1(T(1,0)M)=0c1(T(1,0)M)=0. If MM admits a holomorphic Cartan geometry, then we show that MM is holomorphically covered by an abelian variety.  相似文献   

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The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (TT), frequency (ww), Onsager coefficient (γγ) and external magnetic field (HH) near the second-order (Tc)(Tc) and first-order (Tt)(Tt) phase transition temperatures are examined for given coordination numbers qq on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)(α). Our investigations revealed that only one peak is obtained near TtTt and three peaks are found near TcTc when the Onsager coefficient is varied at a given constant frequency for q=3q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4q=3,4 and 6 near TcTc. The sound attenuation peaks are observed near TtTt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.  相似文献   

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Magnetic properties of the bond and crystal field dilution spin-3/2 Blume–Capel model in an external magnetic field (h)(h) on simple cubic lattice are studied by using the effective field theory. In the m−TmT plane, the degeneracy of the magnetization (m)(m) is affected by the concentration of bond or crystal field dilution at low temperature (T)(T). The magnetization curves can appear to fluctuate in certain regions of negative crystal field. In the m−hmh plane, the initial magnetization curve has an irregular behavior due to the introduction of bond dilution. The crystal field dilution has the influence on the process of magnetic domain displacement. In the χ−hχh plane, there exists one susceptibility (χ)(χ) shoulder and one step for different negative crystal field. The susceptibility curve takes on the feature of multi-peaks distribution under bond and crystal field dilution conditions.  相似文献   

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