Given a closed polygon P having n edges, embedded in R, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface embedded in R d having P as its geometric boundary. More generally we obtain such bounds for a triangulated (locally flat) PL surface having P as its boundary which is immersed in R and whose interior is disjoint from P . The most ...

We construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a 1-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two ...

In this paper we construct a new family of flat Minkowski planes of group dimension 3. These planes share the positive half with the classical real Minkowski plane and admit simple groups of automorphisms isomorphic to PSL2ðRÞ acting diagonally on the torus. We further determine the full automorphism groups and the Klein–Kroll types of these flat Minkowski planes. 2000 Mathematics Subject Class...

We study a flat spacetime with a compact spatial dimension and dispute the claim of Bansal, Laing, and Sriharan that a local experiment can determine whether or not an inertial observer is “privileged” in this spacetime.

We give an elementary proof that the model category of dg-categories over a ring of flat dimension 0 is left proper and we provide a construction of simplicial resolutions in dg-categories, given by categories of Maurer-Cartan elements.

We study a flat spacetime with one compact spatial dimension and dispute the claim of Bansal, Laing, and Sriharan that a local experiment can determine whether or not an inertial observer is “privileged” in this spacetime.

We solve the σ2-Yamabe problem for a non locally conformally flat manifold of dimension n > 8. Dedicated to Professor W. Y. Ding on the occasion of his 60’s birthday

In this paper we find the most general self-similar, homogeneous and isotropic, Ricci flat cosmologies in 5D. These cosmologies show a number of interesting features: (i) the field equations allow a complete integration in terms of one arbitrary function of the similarity variable, and a free parameter; (ii) the three-dimensional spatial surfaces are flat; (iii) the extra dimension is spacelike...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...

Let R be a Noetherian local ring and Ω an arbitrary R-module of finite depth and finite projective dimension. The flat dimension of Ω is at least depth(R)−depth(Ω) with equality in the following cases: (i) Ω is finitely generated over some Noetherian local R-algebra S; (ii) dim(R) = 1; (iii) dim(R) = 2 and Ω is separated; (iv) R is CohenMacaulay, dim(R) = 3 and Ω is complete.