scholarly journals Examples of compact Einstein four-manifolds with negative curvature

2020 ◽  
Vol 33 (4) ◽  
pp. 991-1038
Author(s):  
Joel Fine ◽  
Bruno Premoselli
Keyword(s):  
Negative Curvature ◽  
Four Manifolds

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Manifolds with wells of negative curvature

1991 ◽  
Vol 103 (1) ◽  
pp. 471-495 ◽  
Author(s):  
K. D. Elworthy ◽  
Steven Rosenberg
Keyword(s):  
Negative Curvature

scholarly journals A Geometric Study of Wasserstein Spaces: Isometric Rigidity in Negative Curvature

2015 ◽  
Vol 2016 (5) ◽  
pp. 1368-1386 ◽  
Author(s):  
Jérôme Bertrand ◽  
Benoît R. Kloeckner
Keyword(s):  
Negative Curvature ◽  
Geometric Study
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