Journal of Geometry and Physics最新文献

In this paper, we study the weighted p-basic harmonic forms on a weighted Riemannian foliation $(M,g,F,e^{-f}\nu )$ for some basic function f. At the same time, we prove that there is no non-trivial $L_f^p$-weighted p-basic harmonic form under some assumptions about the generalized weighted curvature. Finally, we consider the Liouville type theorem for ${(F,F^{\prime })}_{(p,f)}$-harmonic map between $(M,g,F,e^{-f}\nu )$ and $(M^{\prime },g^{\prime },F^{\prime })$ as applications.

In this paper, we treat the quaternionic functional calculus for right linear quaternionic operators whose components do not necessarily commute and develop a theory of quaternionic non-negative operator, spherical sectorial operator and dissipative operator via S-resolvent kernels in quaternionic locally convex spaces (short for $q.l.c.s$.). The notions of quaternionic non-negative operators and quaternionic (m-)dissipative operators are introduced via S-resolvent operators and $H$-valued inner product on Hilbert $H$-bimodule. By choosing the suitable spherical sector, the spherical sectorial operator is introduced to establish the relationship with the quaternionic non-negative operator. It is crucial to note that the quaternionic operators we consider do not necessarily commute.

In this paper we consider periodic orbit pairs contributing in the third order of the spectral form factor in the Hadamard-Gutzwiller model. We prove that periodic orbits involving two 2-encounters in certain structures have partner orbits, which together with original ones form orbit pairs and contribute in the third order of the spectral form factor. The action differences are estimated at $\ln (1+u_1{s}_1)(1+u_2{s}_2)$ with explicit error bounds, where $(u_1,s_1)$ and $(u_2,s_2)$ are the coordinates of the piercing points. A symbolic dynamics for orbit pairs via conjugacy classes is also established.

This paper explores the situation regarding the zeros of a proper homothetic vector field X on a 4-dimensional manifold admitting a metric of neutral signature. The types of such zeros are described in terms of the algebraic types of the Ricci tensor and Weyl tensor at the said zero together with a geometrical description of the set of such zeros. A comparison is made between the situation occurring here and that for positive definite and Lorentz signatures. Examples are given to show that many of the theoretical possibilities derived for such zeros actually exist.

In this paper, we prove the spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends and a non-compact boundary. Moreover, we demonstrate a quantitative shielding theorem, subject to the tilted boundary dominant energy condition. Our results are established by solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.

The primary focus of the current study is to explore the geometrical properties of the Vaidya-Bonner-de Sitter (briefly, VBdS) spacetime, which is a generalization of Vaidya-Bonner spacetime, Vaidya spacetime and Schwarzschild spacetime. In this study we have shown that the VBdS spacetime describes various types of pseudosymmetric structures, including pseudosymmetry due to conformal curvature, conharmonic curvature and other curvatures. Additionally, it is shown that such a spacetime is 2-quasi-Einstein, Einstein manifold of level 3, generalized Roter type, and that conformal 2-forms are recurrent. The geometric features of the Vaidya-Bonner spacetime, Vaidya spacetime, and Schwarzschild spacetime are obtained as a particular instance of the main determination. It is further established that the VBdS spacetime admits almost Ricci soliton and almost η-Yamabe soliton with respect to non-Killing vector fields. Also, it is proved that such a spacetime possesses generalized conharmonic curvature inheritance. It is interesting to note that in the VBdS spacetime the tensors $Q(T,R)$, $Q(S,R)$ and $Q(g,R)$ are linearly dependent. Finally, this spacetime is compared with the Vaidya-Bonner spacetime with respect to their admitting geometric structures, viz., various kinds of symmetry and pseudosymmetry properties.

We consider the moduli space of stable parabolic Higgs bundles of rank r and fixed determinant, and having full flag quasi-parabolic structures over an arbitrary parabolic divisor on a smooth connected complex projective curve X of genus g, with $g\ge 2$. The group Γ of r-torsion points of the Jacobian of X acts on this moduli space. We describe the connected components of the various fixed point loci of this moduli under non-trivial elements from Γ. When the Higgs field is zero, or in other words when we restrict ourselves to the moduli of stable parabolic bundles, we also compute the orbifold Euler characteristic of the corresponding global quotient orbifold. We also describe the Chen–Ruan cohomology groups of this orbifold under certain conditions on the rank and degree, and describe the Chen–Ruan product structure in special cases.

We find the twisted extensions of the symmetry algebra of the 2D Euler equation in the vorticity form and use them to construct new Lax representation for this equation. Then we generalize this result by considering the transformation Lie–Rinehart algebras generated by finite-dimensional subalgebras of the symmetry algebra and derive a family of Lax representations for the Euler equation. The family depends on functional parameters and contains a non-removable spectral parameter.

In this work the problem of the consistent treatment of multidimensional quadratic Hamiltonians is analyzed and developed from the geometric point of view. To this end, two approaches to the treatment for the problem are studied and developed: the pure matrix representation that involves Madelung type transforms (maps), and the evolution type based in a group manifold endowed with the symplectic groups and their coverings. Some of our goals is to introduce important geometric and group theoretical tools in the proposed approaches, such as Fermi normal coordinates in the first and a generalization of the method of nonlinear realizations in the second one. Several interesting results appear and some examples of application of these concepts in different physical scenarios are developed and presented such as the relationship with the Zeldovich approximation for the dynamic of large-scale cosmological structure, the classic case of Gertsner waves or the evolution problem with an inverted Hamiltonian of Caldirola-Kanai type.

In this article we give a condition, depending on the renormalized volume of a four-dimensional Poincaré-Einstein manifold, which implies that the TT-gauge-fixed linearised Einstein operator is non-degenerate.