In string-inspired effective actions, representing the low-energy bulk dynamics of brane/string theories, the higher-curvature ghost-free Gauss-Bonnet combination is obtained by local field redefinitions which leave the (perturbative) string amplitudes invariant. We show that such redefinitions lead to surface terms which induce curvature on the brane world boundary of the bulk spacetime. ∗ ema...

In classical differential geometry, surfaces of constant mean curvature (CMC surfaces) have been studied extensively [1]. As a generalization of CMC surfaces, Bobenko [2] introduced the notion of surface with harmonic inverse mean curvature (HIMC surface). He showed that HIMC surfaces admit Lax representation with variable spectral parameter. In [5], Bobenko, Eitner and Kitaev showed that the G...

We study a gravity model where a tensionful codimension-one threebrane is embedded in a bulk with infinite transverse length. We find that 4D gravity is induced on the brane already at the classical level if we include higher-curvature (Gauss-Bonnet) terms in the bulk. Consistency conditions appear to require a negative brane tension as well as a negative coupling for the higher-curvature terms.

An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 256(3) grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfa...

Curvature measure is one of the basic notion in the theory of convex bodies. Together with surface area measures, they play fundamental roles in the study of convex bodies. They are closely related to the differential geometry and integral geometry of convex hypersurfaces. Let Ω is a bounded convex body in R with C2 boundary M , the corresponding curvature measures and surface area measures of ...

We prove nonexistence of nonconstant local minimizers for a class of functionals, which typically appears in the scalar two-phase field model, over a smoothN−dimensional Riemannian manifold without boundary with non-negative Ricci curvature. Conversely for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative we prove existence of nonconstant local ...

We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N -dimensional Riemannian manifolds without boundary and nonnegative Ricci curvature. Conversely, for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative, we prove the existence of nonconstant l...

In this paper we study surfaces in Euclidean 3-space foliated by pieces of circles and that satisfy a Weingarten condition of type aH+bK = c, where a, b and c are constant and H and K denote the mean curvature and the Gauss curvature respectively. We prove that a such surface must be a surface of revolution, a Riemann minimal surface or a generalized cone.

This paper presents an elegant contact dynamics model in screw bondgraph form. It can model the contact between any two objects of finite curvature. It does so by defining a Gauss frame on the surfaces of both objects in the points that are closest to each other. Then it describes how the Gauss frames move as the objects move relative to each other. This is called the contact kinematics. The co...

Let (M,g) be a compact Riemannian manifold. The conformal class of g consists of all metrics g̃ = e2ug for any smooth function u. A central theme in conformal geometry is the study of properties that are common to all metrics in the same conformal class, and the understanding and classification of all the conformal classes. For this purpose it is often useful to be able to single out a unique re...