Let N p (c) be an (n+p)-dimensional connected Lorentzian space form of constant sectional curvature c and φ : M → N p (c) an n-dimensional spacelike submanifold in N p (c). The immersion φ : M → N p (c) is called a Willmore spacelike submanifold in N p (c) if it is a critical submanifold to the Willmore functional W (φ) = ∫

In previous work [Meese et al. (1995). Vision Research, 35, 2879-2888)] we showed that one-dimensional (1D) speed gradients are sufficient to produce a compelling impression of surface slant. Summing a 1D vertical shearing gradient or, less intuitively, a 1D horizontal shearing gradient with a random field of horizontally translating dots produces perceived slant about a horizontal axis. Simila...

In 4 experiments, the authors varied the extent and nature of participant movement in a virtual environment to examine the influence of action on estimates of geographical slant. Previous studies showed that people consciously overestimate hill slant but can still accurately guide an action toward the hill (D. R. Proffitt, M. Bhalla, R. Gossweiler, & J. Midgett, 1995). Related studies suggest t...

Existing techniques for obtaining shape from texture estimate tilt and slant via a single computational mechanism. These techniques do not take advantage of the fact that tilt is relatively easy to estimate, and slant can be estimated more easily once tilt is known. This paper introduces the adaptive bisector method, which allows tilt and slant to be calculated separately, and by different comp...

We construct a new index of media slant that measures whether a news outlet’s language is more similar to a congressional Republican or Democrat. We apply the measure to study the market forces that determine political content in the news. We estimate a model of newspaper demand that incorporates slant explicitly, estimate the slant that would be chosen if newspapers independently maximized the...

A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite ...

We write down the local equations that characterize the sub-manifolds N of a Dirac manifold M which have a normal bundle that is either a coisotropic or an isotropic submanifold of T M endowed with the tangent Dirac structure. In the Poisson case, these formulas prove again a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of T M with the tangent Poisson s...