Non-flat interactive displays have one very distinct property that differs from the touch displays we use on tablets or smartphones: the spatial structure that defines their non-flatness. In this paper, we investigate one specific class of spatial structure – planes bent in one dimension with both concave and convex curvature. We study horizontal pointing and dragging along those bends to see h...

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a...

We present an N = 1 superfield formulation of supersymmetric gauge theories with a compact extra dimension. The formulation incorporates the radion superfield and allows to write supersymmetric theories on warped gravitational backgrounds. We apply it to study the breaking of supersymmetry by the F -term of the radion, and show that, for flat extra dimensions, this leads to the same mass spectr...

We present two families of exterior differential systems (EDS) for causal embeddings of orthonormal frame bundles over Riemannian spaces of dimension q = 2, 3, 4, 5.... into orthonormal frame bundles over flat spaces of higher dimension. We calculate Cartan characters showing that these EDS are dynamical field theories. The first family includes a nonisometric embedding EDS for classical Einste...

We provide the exact time-dependent cosmological solutions in the RandallSundrum (RS) setup with bulk matter, which may be smoothly connected to the static RS metric. In the static limit of the extra dimension, the solutions are reduced to the standard Friedmann equations with a warp factor. In view of our solutions, we also propose an explanation for how the extra dimension is stabilized in sp...

We examine homogeneous solitons of the ambient obstruction flow and, in particular, prove that any compact soliton with constant scalar curvature is trivial. Focusing on dimension 4, we show gradient Bach steady must be flat, and only non-Bach-flat shrinking are product metrics $$\mathbb {R}^2\times S^2$$ {R}^2 \times H^2$$ . also construct a expanding soliton. establish number results for to g...

We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modi...

The statement often called the Gromov-Lawson-Rosenberg Conjecture asserts that a manifold with finite fundamental group should admit a metric of positive scalar curvature except when the KO∗-valued index of some Dirac operator with coefficients in a flat bundle is non-zero. We prove spin and oriented non-spin versions of this statement for manifolds (of dimension ≥ 5) with elementary abelian fu...

We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Selfavoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all tem...

We report on spectral-domain and time-domain measurements and numerical calculations of group velocities in a photonic crystal coupled waveguide, where the unique guided mode band structure has a flat band region within the photonic band gap allowing for slow light observation. The spectral dependence of group velocity, which is measured by interference method, indicates the existence of slow l...