Lorentzian Geometry of the Heisenberg GroupGeometriae Dedicata - Tập 118 - Trang 133-140 - 2006
N. Rahmani, S. Rahmani
In this work we prove the existence of totally geodesic two-dimensional foliation on the Lorentzian Heisenberg group H
3. We determine the Killing vector fields and the Lorentzian geodesics on H
3.
Cusp closing of hyperbolic manifoldsGeometriae Dedicata - Tập 59 - Trang 147-156 - 1996
S. V. Buyalo, V. L. Kobel'skii
A general method to produce infinitely many pairwise homotopically nonequivalent closed manifolds using the cusp closing construction is presented. An infinite sequence of closed homotopically nonequivalent real analytic Riemannian 5-manifolds with uniformly bounded volumes and uniformly bounded nonpositive sectional curvatures, which are allowed to vanish along codimension two submanifolds only, ...... hiện toàn bộ
A counterexample to a ‘simplex algorithm’ for convex bodiesGeometriae Dedicata - Tập 11 - Trang 475-488 - 1981
S. Gallivan, R. J. Gardner
A counterexample, in E
3, is given to the following conjecture. Suppose f
* is a linear functional, and e an exposed point of a convex body K such that f
* does not attain its maximum on K at e; then there is an f
*-strictly increasing path in the one-skeleton of K emanating from e. The counterexample shows that a certain generalized ‘simplex algorithm’ fails. Furthermore for a different linear fu...... hiện toàn bộ
Barth type vanishing theoremGeometriae Dedicata - Tập 141 - Trang 87-92 - 2008
F. Laytimi, D. S. Nagaraj
In this paper we give a vanishing result for cohomology groups of symmetric powers of the co-normal bundle of a non-degenerate smooth subvariety X of projective space, then we use this theorem to give a Barth type vanishing theorem.
Hyperbolic twisted torus linksGeometriae Dedicata - Tập 217 - Trang 1-16 - 2023
Thiago de Paiva
The twisted torus link T(p, q; r, s) is obtained by twisting r parallel strands of the (p, q)-torus link a total of s full times. In this paper we find all twisted torus links which are hyperbolic for
$$\vert s\vert >3$$
.
A note on nodal determinantal hypersurfacesGeometriae Dedicata - Tập 208 - Trang 97-111 - 2020
Sz-Sheng Wang
We prove that a general determinantal hypersurface of dimension 3 is nodal. Moreover, in terms of Chern classes associated with bundle morphisms, we derive a formula for the intersection homology Euler characteristic of a general determinantal hypersurface.
NachrufGeometriae Dedicata - Tập 13 - Trang 113-113 - 1982
Karl Strambach
Maximal extension of conformally flat globally hyperbolic space–timesGeometriae Dedicata - Tập 174 - Trang 235-260 - 2014
Clara Rossi Salvemini
The notion of maximal extension of a globally hyperbolic space–time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein’s equations of general relativity. Choquet-Bruhat and Geroch proved (Commun Math Phys 14:329–335, 1969) that if the Cauchy problem has a local solution, this solution has a unique maximal extension. Since the causal structure of a space–ti...... hiện toàn bộ
Integral Geometry of Tame SetsGeometriae Dedicata - Tập 82 - Trang 285-323 - 2000
Ludwig Bröcker, Martin Kuppe
Curvature measures on certain tame Whitney-stratified sets are defined as coefficients of modified volume-growth polynomials. Stratified Morse theory yields alternative descriptions of these curvature measures for tame (possibly highly singular) sets. From this we obtain a generalized Gauss–Bonnet formula and various kinematic formulas. Finally, for O-minimal sets it is shown that curvature measur...... hiện toàn bộ