scholarly journals A solution to Flinn’s conjecture on weakly expansive flows

2020 ◽  
pp. 1-7
Author(s):  
HIEN MINH HUYNH
Keyword(s):  
Riemann Surfaces ◽  
Negative Curvature ◽  
Constant Negative Curvature ◽  
Horocycle Flow ◽  
Compact Riemann Surfaces ◽  
Phd Thesis ◽  
Expansive Flows

In L. W. Flinn’s PhD thesis published in 1972, the author conjectured that weakly expansive flows are also expansive flows. In this paper we use the horocycle flow on compact Riemann surfaces of constant negative curvature to show that Flinn’s conjecture is not true.

scholarly journals Factors of horocycle flows

1982 ◽  
Vol 2 (3-4) ◽  
pp. 465-489 ◽  
Author(s):  
Marina Ratner
Keyword(s):  
Finite Volume ◽  
Tangent Bundle ◽  
Negative Curvature ◽  
Constant Negative Curvature ◽  
Horocycle Flow ◽  
Unit Tangent Bundle

AbstractWe classify up to an isomorphism all factors of the classical horocycle flow on the unit tangent bundle of a surface of constant negative curvature with finite volume.

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.

A Hodge theoretic projective structure on compact Riemann surfaces

2021 ◽  
Vol 149 ◽  
pp. 1-27
Author(s):  
Indranil Biswas ◽  
Elisabetta Colombo ◽  
Paola Frediani ◽  
Gian Pietro Pirola
Keyword(s):  
Riemann Surfaces ◽  
Projective Structure ◽  
Compact Riemann Surfaces

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

scholarly journals Isospectral flat connexions

2013 ◽  
Vol 31 (2) ◽  
pp. 279
Author(s):  
S. Srinivas Rau ◽  
Sudhamsh Reddy
Keyword(s):  
Riemann Surfaces ◽  
Higher Rank ◽  
Compact Riemann Surfaces

Isospectral flat connexions are constructed for higher rank bundlesover compact Riemann surfaces

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