arXiv research

New approach to T-duality using Courant algebroids.

For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For sy…

Defines T-duality and generalised Ricci flow relations using Courant algebroid relations.

New criterion for solving inverse Hessian equations, including J-equation.

Quasi-isometries in horospherical products are close to product maps.

Constructs brane current algebras from QP-manifolds, generalizing string currents.

We study supersymmetric AdS$_D$ backgrounds of eleven-dimensional or type II supergravity preserving $\mathcal{N}$ supersymmetries using generalised geometry. We show that a large class correspond precisely to spaces admitting a generalised $G_{D,\mathcal{N}}$ structure with a weak integrability condition, which we cal…

Study shows saddle connection graph's geometry and quasi-isometry properties.

This research quantifies neural networks using magnitude, a topological invariant.

Introduces halo products and studies their geometric properties.

The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields on pseudo-Riemannian quadrics. A para-Kaehler twisted anti-isometry is used to …

In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$. Then the pair $(H,g_H)$ defines a sub-Riemannian structure on $M$. We call …

We study supersymmetric deformations of N = 4 quantum mechanics with a Kahler target space admitting a holomorphic isometry. We show that the twisted mass deformation generalises to a deformation constructed from matrix-valued functions of the moment map, which obey the Nahm equations. We also explain how N = 4 supersy…

We introduce a notion of the twist of an isometry of the hyperbolic plane. This twist function is defined on the universal covering group of orientation-preserving isometries of the hyperbolic plane, at each point in the plane. We relate this function to a function defined by Milnor and generalised by Wood. We deduce v…

We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two different viewpoints, one with constructive techniques to enumerate such tiling…

The paper establishes correspondences between quaternionic spinors, Minkowski flags, and hyperbolic horospheres.

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under minimal regularity hypothesis. In particular we show that an isometry between $C^{k,α}$-smooth (or partially smooth) Finsler metrics, with $k+α>0$, $k\in \mathbb{N} \cup \{0\}$, and $0 \leq α\leq 1$ is necessary a diffeomorphism of class $C^{k+1…

Generalizes skyrmion theory to gauged maps with $G$-action.

Develops a method to deform metrics on manifolds with non-compact boundaries.

Researchers extend parametrization of Margulis spacetimes using strip deformations.

A nonnegative number d_infinity, called asymptotic dimension, is associated with any metric space. Such number detects the asymptotic properties of the space (being zero on bounded metric spaces), fulfills the properties of a dimension, and is invariant under rough isometries. It is then shown that for a class of open …

In this article we survey and describe various aspects of the geometry and arithmetic of Kleinian groups - discrete nonelementary groups of isometries of hyperbolic $3$-space. In particular we make a detailed study of two-generator groups and discuss the classification of the arithmetic generalised triangle groups (and…

Study of MHD equilibria with orientation-reversing symmetry, showing all orbits are periodic.

An explicit surjection from a set of (locally defined) unconstrained holomorphic functions on a certain submanifold of (Sp_1(C) \times C^{4n}) onto the set HK_{p,q} of local isometry classes of real analytic pseudo-hyperkähler metrics of signature (4p,4q) in dimension 4n is constructed. The holomorphic functions, calle…

The study classifies Heintze groups up to isometry and quasi-isometry in low dimensions.

Given an ideal triangulation of a connected 3-manifold with non-empty boundary consisting of a disjoint union of tori, a point of the deformation variety is an assignment of complex numbers to the dihedral angles of the tetrahedra subject to Thurston's gluing equations. From this, one can recover a representation of th…

The paper generalizes Cartan Geometry using Polacek and Siegel's approach.

Constructs a unique Levi-Civita connection for generalised metrics.

The paper applies generalised geometry to semi-Riemannian immersions and hypersurfaces.

Differential structure on partial isometries over Grassmannian constructed.

Given an SO(3)-bundle with connection, the associated two-sphere bundle carries a natural closed 2-form. Asking that this be symplectic gives a curvature inequality first considered by Reznikov. We study this inequality in the case when the base has dimension four, with three main aims. Firstly, we use this approach to…

Lifts isometries in orbit spaces for compact groups.

Sharp stability of isometries on Heisenberg group proven.

Study reveals structure of isometry group for specific manifolds.

Study on holomorphic isometries between complex domains, revealing geometric properties.

We introduce and study the notion of relative rigidity for pairs $(X,\JJ)$ where 1) $X$ is a hyperbolic metric space and $\JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $\JJ$ the collection of parabolics 3) $X$ is a higher rank symmetric space and $\JJ$ an equivariant collection of ma…

Study finds all isometries for specific Lie groups.

Explicit isometry groups found for nearly Kähler manifolds.

Compact Lie groups have compact isometry groups with pseudo-Riemannian metrics.

Proper holomorphic isometries between Bergman domains are biholomorphisms.

Every element of PU(2,1) can be decomposed into at most 4 special elliptic isometries.

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised Kähler geometry for $(2,2)$, generalised hyperkähler geometry for $(4,2)$, strong Kähler with torsion geometry for $(2,1)$ and strong hyperkähler with torsion geometry f…

Computes Weyl group of Kähler toric manifold isometries.

Study of isometries in spacetimes without observer horizons.

Derives curvature conditions for spatial isotropy without field equations.

The paper explores conditions for constructing and extending infinitesimal isometries on special sub-Riemannian manifolds.

Characterizes self-isometries of Riemannian metrics on compact manifolds.

We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group contains an index two subgroup of isometries that extend.