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 $$\vert s\vert >3$$ .
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