共查询到20条相似文献,搜索用时 15 毫秒
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He Longguang 《Reports on Mathematical Physics》2004,53(1):123-142
This paper gives the definition of Dirac-Nijenhuis manifolds (DN-manifolds). It discusses their properties and the relations among DN-manifolds, Poisson-Nijenhuis manifolds (PN-manifolds) and presymplectic-Nijenhuis manifolds (ΩN-manifolds). 相似文献
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We propose a system of two equations which, when some of its parameters vanish, separates into two equations describing independent one-dimensional Toda chains. The system has its foundation in the discrete transformations of the Landau-Lifshitz equation which is closely connected with elliptic curves. Nontrivial solutions of the system are found in an explicit form. 相似文献
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We obtain some results on symmetries of sub-Riemannian surfaces. In case of a contact sub-Riemannian surface we base on invariants found by Hughen [15]. Using these invariants, we find conditions under which a sub-Riemannian surface does not admit symmetries. If a surface admits symmetries, we show how invariants help to find them. It is worth noting, that the obtained conditions can be explicitly checked for a given contact sub-Riemannian surface. Also, we consider sub-Riemannian surfaces which are not contact and find their invariants along the surface where the distribution fails to be contact. 相似文献
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Yi Cheng 《Letters in Mathematical Physics》1996,36(1):35-44
It is known that second Hamiltonian structures of the KP hierarchy are parameterized by a continuous complex parameter q and correspond to the W-infinite algebra of W
infKP
sup(q)
. In this Letter, by constructing a Miura map, we first show a generalized decomposition theorem to the second Hamiltonian structures and then establish a relation between those structures which corresponds to values (q+1) and q of the parameter, respectively. This discussion also gives a better understanding to the structures of W
infKP
sup(q)
, its reduced
algebras, and their free fields realizations. 相似文献
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Yi Cheng 《Letters in Mathematical Physics》1995,33(2):159-169
TheW
KP
(N)
algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW
KP
(N)
can also be decomposed toN independent copies ofW
KP
(1)
algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW
KP
(1)
. In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW
KP
(N)
in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R)
k
algebras with levelk = 1. By reductions, we give similar results forW
(N)
andW
3
(2)
algebra. 相似文献
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Radul has recently introduced a map from the Lie algebra of differential operators on the circle of W
n
. In this Letter, we extend this map to W
KP
(q)
, a recently introduced one-parameter deformation of WKP - the second Hamiltonian structure of the KP hierarchy. We use this to give a short proof that W is the algebra of additional symmetries of the KP equation. 相似文献
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J. Lehmann-Lejeune in [J. Lehmann-Lejeune, Cohomologies sur le fibré transverse à un feuilletage, C.R.A.S. Paris 295 (1982), 495–498] defined on the transverse bundle V to a foliation on a manifold M, a zero-deformable structure J such that J2=0 and for every pair of vector fieldsX,Y on M: [JX,JY]−J[JX,Y]−J[X,JY]+J2[X,Y]=0. For every open set Ω of V, J. Lehmann-Lejeune studied the Lie Algebra LJ(Ω) of vector fields X defined on Ω such that the Lie derivative L(X)J is equal to zero i.e., for each vector field Yon Ω: [X,JY]=J[X,Y] and showed that for every vector field X on Ω such thatX∈KerJ, we can write X=∑[Y,Z] where ∑is a finite sum and Y,Z belongs to LJ(Ω)∩(KerJ|Ω). 相似文献
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In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle Vk to a decreasing family of k foliations Fi on a manifold M. We have shown that there exists a (1,1) tensor J of Vk such that Jk≠0, Jk+1=0 and we defined by LJ(Vk) the Lie Algebra of vector fields X on Vk such that, for each vector field Y on Vk, [X,JY]=J[X,Y]. 相似文献
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L. A. Ibort 《Letters in Mathematical Physics》1992,25(2):131-137
Universal hyper-Kähler spaces are constructed from Lie groups acting on flat Kähler manifolds. These spaces are used to describe the moduli space of solutions of Hitchin's equation — self-duality equations on a Riemann surface — as the contangent bundle of the moduli space of flat connections on a Riemann surface. 相似文献
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Diffieties formalize geometrically the concept of differential equations. We introduce and study Hamilton–Jacobi diffieties. They are finite dimensional subdiffieties of a given diffiety and appear to play a special role in the field theoretic version of the geometric Hamilton–Jacobi theory. 相似文献
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Introducing the notion of an admissible graded Lie subalgebra A of the Nijenhui-Richardson algebra A(V) of the vector space V, it is shown that each cohomology class of a subcomplex C
A
of the Chevalley-Eilenberg complex (C
0
M), extends in a cononical way as a graded cohomology class of weight — 1 of A. Applying this when V is the space N of smooth functions of a smooth manifold M, shows that the de Rham cohomology of M is induced by the graded cohomology of weight — 1 of the Schouten graded Lie algebra of M. This allows us to construct explicitly all 1-differential, nc formal deformations of the Poisson bracket of a symplectic manifold. The construction also applies for an arbitrary Poisson manifold but leads to only part of these deformations when the structure degenerates, as shown by an example. 相似文献
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We show that any Weyl curvature model can be geometrically realized by a Weyl manifold. 相似文献
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We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z2)n-graded commutative associative algebra A. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonné determinant of quaternionic matrices, but in general our quaternionic determinant is different. We show that the graded determinant of purely even (Z2)n-graded matrices of degree 0 is polynomial in its entries. In the case of the algebra A=H of quaternions, we calculate the formula for the Berezinian in terms of a product of quasiminors in the sense of Gelfand, Retakh, and Wilson. The graded trace is related to the graded Berezinian (and determinant) by a (Z2)n-graded version of Liouville’s formula. 相似文献
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Amine M. El Gradechi 《Letters in Mathematical Physics》1995,35(1):13-26
In this Letter, we show how the complete geometric quantization extends to specific supersymplectic supermanifolds. More precisely, we extend this procedure to OSp(1/2)-coadjoint orbits, which are graded extensions of elliptic Sp(2, )-coadjoint orbits. Our approach exploits results obtained in a previous work, where the notion of a super-Kähler supermanifold was defined, and the former orbits were shown to be nontrivial examples of such a notion. As their underlying Kähler manifolds, these supermanifolds carry a natural (super-Kähler) polarization, a crucial notion that was so far lacking. Geometric quantization leads here to a nontrivial representation of osp(1/2), which is realized in a space of square integrable holomorphic sections of a super-Hermitian complex line bundle sheaf-with-connection over the homogenous space OSp(1/2)/U(1). 相似文献
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