Journal of Geometry and Physics最新文献

We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems – as a ($0+1$)-dimensional field – and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory.

In this article, we introduce quasi-Bach tensor and correspondingly introduce almost quasi-Bach solitons, thereby generalizing the existing notion of Bach tensor and almost Bach solitons. We explore some properties of gradient quasi Bach solitons with harmonic Weyl curvature tensor. We study the relationships between Weyl tensor, Cotton tensor, tensor $D$ introduced by Cao, and quasi Bach tensor. We also find the evolution of volume, Einstein metric, Ricci curvature and scalar curvature, under the quasi Bach flow. Our results obtained here extends the results of Bach solitons and Bach flow. Finally, we obtain the characterization of gradient quasi-Bach soliton of type I, a particular quasi Bach soliton, on the product manifolds $S^2\times H^2$ and $R^2\times H^2$. Our exploration generalizes gradient Bach soliton on $R^2\times H^2$ obtained by P. T. Ho, while the gradient soliton on $S^2\times H^2$ is a novel one and is complementary to the results obtained by P. T. Ho.

The paper is devoted to the Barenblatt model of oil and water filtration with an admixture of active reagents. This model is used in oil production for hard-to-recover deposits by chemical flooding. The model is described by a system of two first order nonlinear partial differential equations. Conditions for the Buckley–Leverett function, under which the system is reduced to a linear one using symplectic transformations, are found. This makes possible to find classes of exact general solutions of the Barenblatt system and to solve the Cauchy problem.

We initiate the process by introducing a nonisospectral Lax pair, from which we derive an integrable nonisospectral hierarchy associate with Camassa-Holm equation. Through the inverse scattering transform method, we obtain parameter expressions for the N-soliton solution of the integrable nonisospectral hierarchy associate with Camassa-Holm equation. To derive the precise expression of the solution without the parameters, a coordinate transformation is performed. In order to work out accurately the soliton solution through the Gel'fand-Levitan-Marchenko equation. Finally, we present the graphical representation of the 1-soliton solution and analyze its dynamic behavior.

We consider some new limits for the elliptic hypergeometric integrals on root systems. After the degeneration of elliptic beta integrals of type I and type II for root systems $A_n$ and $C_n$ to the hyperbolic hypergeometric integrals, we apply the limit ${\omega }_1\to -{\omega }_2$ for their quasiperiods (corresponding to $b\to \text{i}$ in the two-dimensional conformal field theory) and obtain complex beta integrals in the Mellin–Barnes representation admitting exact evaluation. Considering type I elliptic hypergeometric integrals of a higher order obeying nontrivial symmetry transformations, we derive their descendants to the level of complex hypergeometric functions and prove the Derkachov–Manashov conjectures for functions emerging in the theory of non-compact spin chains. We describe also symmetry transformations for a type II complex hypergeometric function on the $C_n$-root system related to the recently derived generalized complex Selberg integral. For some hyperbolic beta integrals we consider a special limit ${\omega }_1\to {\omega }_2$ (or $b\to 1$) and obtain new hypergeometric identities for sums of integrals of rational functions.

We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative ${\mathrm{BV}}_{\infty }$-algebra structure satisfying the degeneration property. In the almost Kähler case, this recovers Koszul's BV-algebra, defined for any Poisson manifold. As a consequence, both the Dolbeault and the de Rham cohomologies of any compact Hermitian manifold are canonically endowed with homotopy hypercommutative algebra structures, also known as formal homotopy Frobenius manifolds. Similar results are developed for (almost) symplectic manifolds with Lagrangian subbundles.

We prove that the direct image of an anti-ample vector bundle is anti-ample under any finite flat morphism of non-singular projective varieties. In the second part we prove some properties of big and nef vector bundles. In particular it is shown that the tensor product of a nef vector bundle with a nef and big vector bundle is again nef and big. This generalizes a result of Schneider.

Previously, Wilson surface observables were interpreted as a class of Poisson sigma models. We profit from this construction to define and study the super version of Wilson surfaces. We provide some ‘proof of concept’ examples to illustrate modifications resulting from appearance of odd degrees of freedom in the target.

We present a fully algebraic derivation of the Laguerre polynomials. The derivation is based on the knowledge of the energy eigenvectors of quantum mechanics solution of hydrogen-like atom Schrödinger equation, and a suitable translation operator. The method is purely algebraic since it does not require any analytical calculations.

The geometry of integrable nearly trans-Sasakian manifolds (NST-manifolds) is studied in this paper. In particular, we consider as NST-manifolds with an integrable structure, normal NST-manifolds, and NST-manifolds satisfying the condition $N^{\left(2\right)}=0$. Local structure of such manifolds is also described. We give a classification of NST-manifolds of constant Φ-holomorphic sectional curvature, as well as satisfying the axiom of Φ-holomorphic planes. NST-manifolds with a completely integrable first fundamental distribution are discussed.