Let (M,ω, J) be a compact and connected polarized Hodge manifold, S an isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds. We study the relation between the Weinstein symplectic structure of S and the asymptotics of the the pull-back of the Fubini-Study form under the projectivization of the so-called BPU maps on S.

Homogeneous solutions to topologically massive gravity have been previously found for spacetimes in 2+1 dimensions admitting a simply transitive isometry group. We discuss the case of homogeneous spacetimes in 2+1 dimensions with isotropy, review a technique for classifying them, and examine in each case whether the isometry group has a simply transitive subgroup. We further show that none of t...

We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n ≥ 2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex for all n ≥ 2, and find that it has the collineation group as an index-two subgroup. These results confirm, for the class of pol...

It is consistent with the axioms of set theory that for every metric space X which is isometric to some separable Banach space or to Urysohn’s universal separable metric space U the following holds: (?)X There exists a nowhere meager subspace of X of cardinality א1 and any two nowhere meager subsets of X of cardinality א1 are almost isometric to each other. As a corollary, it is consistent that...

We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k − 1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group c...

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.

Each of the local isometry groups arising in 3d gravity can be viewed as the group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement, and use it as a unifying framework for studying Poisson structures associated with the local isometry groups. We show that, in all cases except for Euclidean signature with positi...

We prove that any isometry between the unit spheres of $C^2$-smooth (more generally, absolutely smooth) smooth Banach spaces extends to a linear spaces. This answers famous Tingley's problem in class $2$-dimensional

Sixty years ago, S. B. Myers and N. E. Steenrod (Ann. of Math. 40 (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a stru ture of Lie group. Re ently A. V. Bagaev and N. I. Zhukova (Siberian Math. J. 48 (2007), 579-592) proved the same result for a Riemannian orbifold. In this paper, we rstly show that the isometry group of a Riemannian manifold M wi...