Results 21 to 30 of about 629 (55)

The topology of closed manifolds with quasi-constant sectional curvature [PDF]

, 2019
We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable positivity ...
Funar, Louis
core   +4 more sources

Bifurcation of periodic solutions to the singular Yamabe problem on spheres [PDF]

, 2015
We obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere, that blow up along a great circle. These are (complete) constant scalar curvature metrics on the complement of $S^1$ inside $S^m$, $m\geq 5$, that are ...
Bettiol, Renato G., Piccione, Paolo, Santoro, Bianca   +2 more
core   +1 more source

Contact structures and Beltrami fields on the torus and the sphere

, 2021
We present new explicit tight and overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible.
Peralta-Salas, Daniel, Slobodeanu, Radu
core   +1 more source

Topological Signals of Singularities in Ricci Flow [PDF]

, 2017
We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow.
Alsing, Paul M., Blair, Howard A., Corne, Matthew, Jones, Gordon, Miller, Warner A., Mischaikow, Konstantin, Nanda, Vidit   +6 more
core   +4 more sources

Constant scalar curvature metrics on connected sums

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 7, Page 405-450, 2003., 2003
The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension n ≥ 3, which minimizes the total scalar curvature on this conformal class. Let (M′, g′) and (M″, g″) be compact Riemannian n‐manifolds. We form their connected sumM′#M″ by
Dominic Joyce
wiley   +1 more source

Bubbles on Manifolds with a U(1) Isometry [PDF]

, 2007
We investigate the construction of five-dimensional, three-charge supergravity solutions that only have a rotational U(1) isometry. We show that such solutions can be obtained as warped compactifications with a singular ambi-polar hyper-Kahler base space
A. Saxena, B. Bates, D. Gaiotto, F. Denef, F. Denef, H. Elvang, I. Bena, I. Bena, I. Bena, I. Bena, I. Bena, I. Bena, I.R. Klebanov, Iosif Bena, J. Ford, J.B. Gutowski, J.P. Gauntlett, L. Grant, M.C.N. Cheng, Nicholas P Warner, Nikolay Bobev, P. Berglund, S.D. Mathur, V. Balasubramanian, V.S. Rychkov   +24 more
core   +2 more sources

De Sitter and Schwarzschild-De Sitter According to Schwarzschild and De Sitter

, 2003
When de Sitter first introduced his celebrated spacetime, he claimed, following Schwarzschild, that its spatial sections have the topology of the real projective space RP^3 (that is, the topology of the group manifold SO(3)) rather than, as is almost ...
A. Aguirre, A. Casher, A. de Oliveira-Costa, A. Strominger, A.A. Bytsenko, A.J.M. Medved, A.L. Besse, B.T. McInnes, Brett McInnes, C. Bennett ., C.G. Callan Jr., D. Chang, E. Schrödinger, G. Efstathiou, G. Efstathiou, G.W. Gibbons, H.B. Lawson, H.K. Eriksen, J. Louko, J. Louko, J. Polchinski, J. Preskill, J.-P. Luminet, J.-P. Uzan, J.A. Wolf, J.M. Maldacena, J.P. van der Schaar, K Schwarzschild, K. Schwarzschild, L. Andersson, L. Dyson, L. Fidkowski, L. Susskind, L.M. Krauss, M. Visser, M.K. Parikh, N. Goheer, P. Kerszberg, P. Scott, R. Bousso, R. Bousso, R.M. Wald, S. Hawking, S. Kobayashi, S. Nojiri, S. Shankaranarayanan, S.W. Hawking, T. Hertog, T. Jacobson, V. Balasubramanian, V. Balasubramanian, W. de Sitter, W. Israel   +52 more
core   +1 more source

Relative cubulation of relative strict hyperbolization

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0)$\operatorname{CAT}(0)$ cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special.
Jean‐François Lafont, Lorenzo Ruffoni
wiley   +1 more source

Relatively Anosov representations via flows II: Examples

Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.
Abstract This is the second in a series of two papers that develops a theory of relatively Anosov representations using the original “contracting flow on a bundle” definition of Anosov representations introduced by Labourie and Guichard–Wienhard. In this paper, we focus on building families of examples.
Feng Zhu, Andrew Zimmer
wiley   +1 more source

Constrained deformations of positive scalar curvature metrics, II

Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 795-862, January 2024.
Abstract We prove that various spaces of constrained positive scalar curvature metrics on compact three‐manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean curvature of the boundary, and our treatment includes both the mean‐convex and the minimal case.
Alessandro Carlotto, Chao Li
wiley   +1 more source