scholarly journals Homologically visible closed geodesics on complete surfaces

2021 ◽  
pp. 1-23
Author(s):  
Simon Allais ◽  
Tobias Soethe
Keyword(s):  
Closed Geodesics ◽  
Möbius Band ◽  
Complete Surfaces

In this paper, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder, a complete Möbius band or a complete Riemannian plane leads to having infinitely many geometrically distinct closed geodesics. In particular, we prove that any complete cylinder with isolated closed geodesics has zero, one or infinitely many homologically visible closed geodesics; this answers a question of Alberto Abbondandolo.

Closed geodesics on complete surfaces

1980 ◽  
Vol 251 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Victor Bangert
Keyword(s):  
Closed Geodesics ◽  
Complete Surfaces

MÖBIUS BAND INTERFEROMETER AND ITS APPLICATION TO FOURIER SPECTROSCOPY

1967 ◽  
Vol 28 (C2) ◽  
pp. C2-91-C2-96
Author(s):  
J. L. PRITCHARD ◽  
H. SAKAI ◽  
W. H. STEEL ◽  
G. A. VANASSE
Keyword(s):  
Fourier Spectroscopy ◽  
Möbius Band

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

scholarly journals Angular self-intersections for closed geodesics on surfaces

2005 ◽  
Vol 134 (02) ◽  
pp. 419-426 ◽  
Author(s):  
Mark Pollicott ◽  
Richard Sharp
Keyword(s):  
Closed Geodesics

scholarly journals Closed geodesics and bounded gaps

2016 ◽  
Vol 287 (1-2) ◽  
pp. 547-554
Author(s):  
Anton Deitmar
Keyword(s):  
Closed Geodesics ◽  
Bounded Gaps

scholarly journals Some properties of Grauert type surfaces

2017 ◽  
Vol 28 (08) ◽  
pp. 1750063 ◽  
Author(s):  
Samuele Mongodi ◽  
Zbigniew Slodkowski ◽  
Giuseppe Tomassini
Keyword(s):  
Convex Space ◽  
Level Sets ◽  
Double Cover ◽  
Classification Theorem ◽  
Stein Space ◽  
Pluriharmonic Function ◽  
Exhaustion Function ◽  
Real Analytic ◽  
Complete Surfaces

In a previous work, we classified weakly complete surfaces which admit a real analytic plurisubharmonic exhaustion function; we showed that, if they are not proper over a Stein space, then they admit a pluriharmonic function, with compact Levi-flat level sets foliated with dense complex leaves. We called these Grauert type surfaces. In this note, we investigate some properties of these surfaces. Namely, we prove that the only compact curves that can be contained in them are negative in the sense of Grauert and that the level sets of the pluriharmonic function are connected, thus completing the analogy with the Cartan–Remmert reduction of a holomorphically convex space. Moreover, in our classification theorem, we had to pass to a double cover to produce the pluriharmonic function; the last part of the present paper is devoted to the construction of an example where passing to a double cover cannot be avoided.

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