We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class obtained by differentiating the star-product with respect to the deformation parameter is seen to be closely related to the characteristic class of the quant...

In this paper, we aim at addressing the globalization problem of Hamilton–DeDonder–Weyl equations on a local k-symplectic framework and introduce notion locally conformal (l.c.k-s.) manifolds. This formalism describes dynamical properties physical systems that behave like multi-Hamiltonian systems. Here, describe Hamiltonian such systems, but also provide global outlook by introducing Lee one-f...

We construct a natural conformally invariant one-form of weight $-2k$ on any $2k$-dimensional pseudo-Riemannian manifold which is closely related to the Pfaffian Weyl tensor. On oriented manifolds, we also one-forms $-4k$ $4k$-dimensional are top degree Pontrjagin forms. The these forms implies that they define functionals space conformal Killing fields. Riemannian show this functional trivial ...

The requirements of conformal invariance for the two point function of the energy momentum tensor in the neighbourhood of a plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary invariant. It is shown that the general solution may contain an arbitrary function of a single conformally invariant variable v, except in dimension 2. The functi...

In this article, we address one of the questions raised by Marc Rieffel in his collection of questions on deformation quantization. The question is whether the K-groups remain the same under flabby strict deformation quantizations. By “deforming” the question slightly, we produce a negative answer to the question. In his collection of questions on deformation quantization [8], Marc Rieffel aske...

The scalars of a N = 1 supersymmetric σ-model in 4 dimensions parametrize a Kähler manifold. This Kähler manifold often takes the form of a tensor product of bundles over a basis manifold. When one of these bundles is a line bundle, the corresponding Kähler form has to satisfy a quantization condition when the topology of the submanifold is non-trivial. This results in a consistency restriction...

Our main results are: (1) The complex and Lagrangian points of a non-complex and nonLagrangian 2n-dimensional submanifold F :M →N , immersed with parallel mean curvature and with equal Kähler angles into a Kähler-Einstein manifold (N, J, g) of complex dimension 2n, are zeros of finite order of sin θ and cos θ respectively, where θ is the common J-Kähler angle. (2) If M is a Cayley submanifold o...

EQUIVARIANT TENSORS ON POLAR MANIFOLDS Ricardo Mendes Wolfgang Ziller, Advisor This PhD dissertation has two parts, both dealing with extension questions for equivariant tensors on a polar G-manifold M with section Σ ⊂ M. Chapter 3 contains the first part, regarding the so-called smoothness conditions: If a tensor defined only along Σ is equivariant under the generalized Weyl group W (Σ), then ...

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

In this paper, we study closed four-dimensional manifolds. particular, show that under various new pinching curvature conditions (for example, the sectional is no more than 5/6 of smallest Ricci eigenvalue) then manifold definite. If restricting to a metric with harmonic Weyl tensor, it must be self-dual or anti-self-dual same conditions. Similarly, if an Einstein metric, either complex project...