Geometriae Dedicata
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Mean curvature flow and Riemannian submersions
Geometriae Dedicata - Tập 184 - Trang 67-81 - 2016
We prove that a sufficient condition ensuring that the mean curvature flow commutes with a Riemannian submersion is that the submersion has minimal fibers. We then lift some results taken from the literature (i.e., Andrews and Baker in J Differ Geom 85:357–395, 2010; Baker in The mean curvature flow of submanifolds of high codimension, 2011; Huisken in J Differ Geom 20:237–266, 1984; Math Z 195:20......
Arithmetic cusp shapes are dense
Geometriae Dedicata - Tập 129 - Trang 47-55 - 2007
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat n-manifold M, we show that the set of similarity classes of flat metrics on M which occur as a cusp cross-section of a hyperbolic (n + 1)-orbifold is dense in the space of similarity classes of flat metrics on M. The set used for density is precisely the set of those classes which arise in......
Lorentzian Geometry of the Heisenberg Group
Geometriae Dedicata - Tập 118 - Trang 133-140 - 2006
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 manifolds
Geometriae Dedicata - Tập 59 - Trang 147-156 - 1996
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, ......
A counterexample to a ‘simplex algorithm’ for convex bodies
Geometriae Dedicata - Tập 11 - Trang 475-488 - 1981
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......
Lie foliations transversely modeled on nilpotent Lie algebras
Geometriae Dedicata - Tập 179 Số 1 - Trang 21-37 - 2015
In this paper, we study on the following two problems of realization for Lie foliations. (1) Which pair of Lie algebras $$(\mathfrak {g},\mathfrak {h})$$ can be realized as a Lie $$\mathfrak {g}$$ -foliation in a closed manifold with the structure Lie algebra $$\mathfrak {h}$$ ? (2) Which pair $$(\mathfrak {g},m)$$ can be realized as a Lie $$\mathfrak {g}$$ -flow in a closed manifold with the stru......
Barth type vanishing theorem
Geometriae Dedicata - Tập 141 - Trang 87-92 - 2008
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 links
Geometriae Dedicata - Tập 217 - Trang 1-16 - 2023
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 hypersurfaces
Geometriae Dedicata - Tập 208 - Trang 97-111 - 2020
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.
Tổng số: 3,072
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