If M is the underlying smooth oriented 4-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics h on M such that W(ω, ω) > 0, where W is the self-dual Weyl curvature of h, and ω is a non-trivial self-dual harmonic 2-form on (M,h). While this open region in the space of Riemannian metrics contains all the known Einstein metrics on M , we show that it contains no others. Conse...

In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open Wilson lines in the new variables formulation of quantum gravity. Up to a divergent factor, it is given by a `shift operator' resembling that in Morales-T ecotl a...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...

A conformal Lie group is a manifold $(M,c)$ such that $M$ has structure and $c$ the defined by left-invariant metric $g$ on $M$. We study Weyl-Einstein structures solvable groups their compact quotients. In case, we show every solvmanifold carrying Einstein. also there are no non-abelian nilpotent groups, classify them in almost abelian case. Furthermore, determine precise list (up to automorph...

General boundary conditions (“branes”) for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morph...

We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical generalizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of...

It has been shown that a Weyl point in superconducting nanostructure may give rise to disk where two quantum states are almost degenerate two-dimensional manifold the parametric space. This opens up possibility of holonomic manipulation: A transformation wave function upon an adiabatic change parameters within manifold. In this paper, we investigate detail opportunities for manipulation disks. ...

This is an expository note on Fedosov’s construction of deformation quantization. Given a symplectic manifold and a connection on it, we show how to calculate the star-product step by step. We draw simple diagrams to solve the recursive equations for the Fedosov connection and for flat sections of the Weyl algebra bundle corresponding to functions. We also reflect on the differences of symplect...

The classical Weyl Law says that if NM(?) denotes the number of eigenvalues Laplace operator on a d-dimensional compact manifold M without boundary are less than or equal to ?, then $${N_M}(\lambda ) = c{\lambda ^d} + O({\lambda ^{d - 1}}).$$ This paper explores prospects improvements remainders products manifolds. In particular we obtain polynomial improvement remainder for spheres, demonstrat...