In this paper we present a novel method to estimate curvature of iso grey-level surfaces in grey-value images. Our method succeeds where isophote curvature fails. There is neither a segmentation of the surface needed nor a parametric model assumed. Our estimator works on the orientation (normal vector) field of the surface. This orientation field and a description of local structure is obtained...

The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the curvature distribution of S 4 space shows an inflated geometry with homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the scalar curvature ...

We study the classical and quantum theory of spherically symmetric spacetimes with scalar field coupling in general relativity. We utilise the canonical formalism of geometrodynamics adapted to the Painleve-Gullstrand coordinates, and present a new quantisation of the resulting field theory. We give an explicit construction of operators that capture curvature properties of the spacetime and use...

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manif...

In this paper, we study the effects of the spontaneous curvature on the static deformation of a vesicle membrane under the elastic bending energy, with prescribed bulk volume and surface area. Generalizing the phase field models developed in our previous works, we deduce a new energy formula involving the spontaneous curvature effects. Several axis-symmetric configurations are obtained through ...

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector fiel...

The vector nature of magnetic fields and the geometrical interpretation of gravity introduced by general relativity guarantee a special coupling between magnetism and spacetime curvature. This magnetogeometrical interaction effectively transfers the tension properties of the field into the spacetime fabric, triggering a variety of effects with profound implications. Given the ubiquity of magnet...

We describe in superspace a classical theory of of two dimensional (1, 1) dilaton supergravity coupled to a super-Liouville field, and find exact super black hole solutions to the field equations that have non-constant curvature. We consider the possibility that a gravitini condensate forms and look at the implications for the resultant spacetime structure. We find that all such condensate solu...

On modifying the gravitational action by addition of higher-derivative terms of curvature, it is obtained that the Ricci scalar behaves as a physical field as well as a geometrical field. Riccion is a particle giving the physical aspect of the Ricci scalar curvature. Here, it is probed about the possibility of riccion being a candidate for cosmic cold dark matter. PACS nos.: 98.80-k; 95.30 C.

Images obtained by drift-scanning with a stationary telescope are affected by the declination-dependent curvature of star trails. The image displacement to curvature and drift rate variation increases with the angular field of view and can lead to significant loss of resolution with modern large-format CCD arrays. We show that these effects can be essentially eliminated by means of an optical c...