International Journal of Geometric Methods in Modern Physics

The equations of motion for the associated constrained Lagrangian to a nonholonomic Lagrangian of second order are computed. The spinning particle subject to the Heisenberg constraint is treated as example and its dynamics is completely described.

The Romanian National Committee of Ethics has detected plagiarism in this article. Its publication status is now retracted with immediate effect from IJGMMP.

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In this paper, we provide infinitely many examples of compact negatively curved almost complex, but not complex, manifolds of complex dimension 2n + 1 or 2n + 2 by using strongly pseudoconvex homogeneous domains in an almost complex manifold. Unlike the Kodaira–Thurston manifold which is the flat case, the first Betti number of the constructed manifolds is even, and their first homology group is, in fact, isomorphic to ℤ⁴ⁿ⁺² or ℤ⁴ⁿ⁺⁴.

We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton operators is also given. From the Hamilton operators we construct another hierarchy of quantum gates via the Cayley transform.

We discuss a class of three-dimensional Chern–Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex four-dimensional hyper-Kähler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V². The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V². Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V².

In this paper we prove the generalized Hyers–Ulam stability of bi-θ-derivations on JB*-triples.

In this paper, we study the space of 3-Lie multipliers on Banach 3-Lie algebras. Moreover, we investigate a characterization of 3-Lie multipliers on commutative and without order Banach 3-Lie algebras. Finally, we establish the stability and superstability of 3-Lie multipliers.

We perform Dirac's canonical analysis for a four-dimensional BF and for a generalized four-dimensional BF theory depending on a connection valued in the Lie algebra of SO(3, 1). This analysis is developed by considering the corresponding complete set of variables that define these theories as dynamical, and we find out the relevant symmetries, the constraints, the extended Hamiltonian, the extended action, gauge transformations and the counting of physical degrees of freedom. The results obtained are compared with other approaches found in the literature.

We study Weyssenhoff spin fluids in Bianchi type-I cosmological models, within the framework of torsional f(R)-gravity; the resulting field equations are derived and discussed in both Jordan and Einstein frames, clarifying the role played by the spin and the non-linearity of the gravitational Lagrangian f(R) in generating the torsional dynamical contributions. The general conservation laws holding for f(R)-gravity with torsion are employed to provide the conditions needed to ensure the preservation of the Hamiltonian constraint and the consequent correct formulation of the associated initial value problem. Examples are eventually given.

Let be a compact orientable smooth manifold admitting an almost complex structure and for (λ, μ) ∈ ℝ² - (0, 0) be the functional defined on the space of the almost Hermitian structure . We discuss the first variational problem of the functional on the space and its subspace in the case where is a product manifold of Sasakian manifolds. Further this paper provides examples of critical Hermitian structures of the functional for various (λ, μ).

Studying the topological aspects of M-branes in M-theory leads to various structures related to Wu classes. First we interpret Wu classes themselves as twisted classes and then define twisted notions of Wu structures. These generalize many known structures, including Pin^- structures, twisted Spin structures in the sense of Distler–Freed–Moore, Wu-twisted differential cocycles appearing in the work of Belov–Moore, as well as ones introduced by the author, such as twisted Membrane and twisted String^c structures. In addition, we introduce Wu^c structures, which generalize Pin^c structures, as well as their twisted versions. We show how these structures generalize and encode the usual structures defined via Stiefel–Whitney classes.

A Riemannian manifold M with an integrable almost product structure P is called a Riemannian product manifold. Our investigations are on the manifolds (M, P, g) of the largest class of Riemannian product manifolds, which is closed with respect to the group of conformal transformations of the metric g. This class is an analogue of the class of locally conformal Kähler manifolds in almost Hermitian geometry. In the present paper we study a natural connection D on (M, P, g) (i.e. DP = Dg = 0). We find necessary and sufficient conditions, the curvature tensor of D to have properties similar to the Kähler tensor in Hermitian geometry. We pay attention to the case when D has a parallel torsion. We establish that the Weyl tensors for the connection D and the Levi-Civita connection coincide as well as the invariance of the curvature tensor of D with respect to the usual conformal transformation. We consider the case when D is a flat connection. We construct an example of the considered manifold by a Lie group where D is a flat connection with non-parallel torsion.

In this paper our aim is mainly to obtain a two-dimensional complex Finsler model of the real gravitation space-time. We prove that, at least in the special case of the weakly gravitational field, this is possible and it leads to some interesting geometrical and physical aspects, such as the study of curvature invariants with respect to complex Berwald frame, intensively studied recently by us for a two-dimensional complex Finsler space. A generalization of the Klein–Gordon equation is proposed and we find solutions which are in concordance to the classical plane wave solution of momentum-energy relation. The last part of the paper is devoted to some applications in which the complex gravitational potential leads to the Bergman metric and to a more general case which leads to a non-purely Hermitian complex Finsler metric, with negative curvature invariant.

In this paper, we introduce a new kind of Riemannian manifold that generalize the concept of weakly Z-symmetric and pseudo-Z-symmetric manifolds. First a Z form associated to the Z tensor is defined. Then the notion of Z recurrent form is introduced. We take into consideration Riemannian manifolds in which the Z form is recurrent. This kind of manifold is named (ZRF)_n. The main result of the paper is that the closedness property of the associated covector is achieved also for rank(Z_kl) > 2. Thus the existence of a proper concircular vector in the conformally harmonic case and the form of the Ricci tensor are confirmed for(ZRF)_n manifolds with rank(Z_kl) > 2. This includes and enlarges the corresponding results already proven for pseudo-Z-symmetric (PZS)_n and weakly Z-symmetric manifolds (WZS)_n in the case of non-singular Z tensor. In the last sections we study special conformally flat (ZRF)_n and give a brief account of Z recurrent forms on Kaehler manifolds.

We perform a class of nonlinear extensions of the reparametrization algebra at arbitrary dimensions. Our extended algebras reproduce in the one-dimensional limit the well-known -ones. We point out the existence of a family of reparametrization invariant functions for which this property is untouched by the extension procedure. This allows to calculate the improvement of the gravitational anomaly within the extended symmetry.

Recently the third author studied horizontal Laplacians in real Finsler vector bundles and complex Finsler manifolds. In this paper, we introduce a class of g-natural metrics G_a,b on the tangent bundle of a Finsler manifold (M, F) which generalizes the associated Sasaki–Matsumoto metric and Miron metric. We obtain the Weitzenböck formula of the horizontal Laplacian associated to G_a,b, which is a second-order differential operator for general forms on tangent bundle. Using the horizontal Laplacian associated to G_a,b, we give some characterizations of certain objects which are geometric interest (e.g. scalar and vector fields which are horizontal covariant constant) on the tangent bundle. Furthermore, Killing vector fields associated to G_a,b are investigated.

Differential operators on Schwartz distributions usually are defined as the transpose of differential operators on test functions. However, they do not exhaust all differential operators. In a general setting, Schwartz distributions on sections of compact support of a vector bundle Y over a smooth manifold X are considered. They constitute a C^∞(X)-module. We follow a generic algebraic notion of differential operators on a module over a commutative ℝ-ring C^∞(X). Such a differential operator on Schwartz distributions is proved to be the transpose of a differential operator on sections of Y → X if and only if it is continuous.