scholarly journals Codimension one minimal foliations and the fundamental groups of leaves

2008 ◽  
Vol 58 (2) ◽  
pp. 723-731 ◽  
Author(s):  
Tomoo Yokoyama ◽  
Takashi Tsuboi
Keyword(s):  
Fundamental Groups ◽  
Codimension One ◽  
Minimal Foliations

scholarly journals Étale Fundamental Groups of Strongly $\boldsymbol{F}$-Regular Schemes

2017 ◽  
Vol 2019 (14) ◽  
pp. 4325-4339 ◽  
Author(s):  
Bhargav Bhatt ◽  
Javier Carvajal-Rojas ◽  
Patrick Graf ◽  
Karl Schwede ◽  
Kevin Tucker
Keyword(s):  
Fundamental Groups ◽  
Codimension One ◽  
Regular Scheme

Abstract We prove that a strongly $F$-regular scheme $X$ admits a finite, generically Galois, and étale-in-codimension-one cover $\tilde X \to X$ such that the étale fundamental groups of $\tilde X$ and $\tilde X_{{\mathrm{reg}}}$ agree. Equivalently, every finite étale cover of $\tilde X_{{\mathrm{reg}}}$ extends to a finite étale cover of $\tilde X$. This is analogous to a result for complex klt varieties by Greb, Kebekus, and Peternell.

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.

QUALITATIVE CHANGES IN RHYTHMIC GYMNASTICS HOOP THROWS FROM THE PERSPECTIVE OF BIOMECHANICAL ANALYSIS

2020 ◽  
pp. 1-8
Author(s):  
Raluca Tanasa
Keyword(s):  
Correlation Coefficient ◽  
Video Recording ◽  
Biomechanical Analysis ◽  
Fundamental Groups ◽  
Horizontal Distance ◽  
Video Recordings ◽  
Rhythmic Gymnastics ◽  
Female Gymnasts ◽  
Execution Technique ◽  
Qualitative Changes

Throws and catches in rhythmic gymnastics represent one of the fundamental groups of apparatus actuation. They represent for the hoop actions of great showmanship, but also elements of risk. The purpose of this paper is to improve the throw execution technique through biomechanical analysis in order to increase the performance of female gymnasts in competitions. The subjects of this study were 8 gymnasts aged 9-10 years old, practiced performance Rhythmic Gymnastics. The experiment consisted in video recording and the biomechanical analysis of the element “Hoop throw, step jump and catch”. After processing the video recordings using the Simi Motion software, we have calculated and obtained values concerning: launch height, horizontal distance and throwing angle between the arm and the horizontal. Pursuant to the data obtained, we have designed a series of means to improve the execution technique for the elements comprised within the research and we have implemented them in the training process. Regarding the interpretation of the results, it may be highlighted as follows: height and horizontal distance in this element have values of the correlation coefficient of 0.438 and 0.323, thus a mean significance of 0.005. The values of the arm/horizontal angle have improved for all the gymnasts, the correlation coefficient being 0.931, with a significance of 0.01. As a general conclusion, after the results obtained, it may be stated that the means introduced in the experiment have proven their efficacy, which has led to the optimisation of the execution technique, thus confirming the research hypothesis.

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

scholarly journals Exploring the landscape of CHL strings on Td

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Dynkin Diagram ◽  
Fundamental Groups ◽  
Computer Algorithms ◽  
Abelian Gauge ◽  
Reduced Rank ◽  
Systematic Exploration ◽  
String Models ◽  
Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

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