A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

2004 ◽  
Vol 2 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Oldřich Kowalski ◽  
Barbara Opozda ◽  
Zdeněk Vlášek
Keyword(s):  
Theoretical Approach ◽  
Locally Homogeneous ◽  
Locally Homogeneous Connections

We Are Able, We Intend, We Act—But We Do Not Succeed: A Theoretical Framework for a Better Understanding of Paradoxical Performance in Sports

2014 ◽  
Vol 8 (4) ◽  
pp. 357-377 ◽  
Author(s):  
Babett H. Lobinger ◽  
Martin K. Klämpfl ◽  
Eckart Altenmüller
Keyword(s):  
Movement Disorders ◽  
Theoretical Approach ◽  
Theoretical Framework ◽  
Diagnostic Methods ◽  
Superior Performance ◽  
Movement Characteristics ◽  
Methodological Approaches ◽  
Sudden Decrease

Paradoxical performance can be described simply as a sudden decrease in a top athlete’s performance despite the athlete’s having striven for superior performance, such as the lost-skill syndrome in trampolining or “the yips” in golf. There is a growing amount of research on these phenomena, which resemble movement disorders. What appears to be missing, however, is a clear phenomenology of the affected movement characteristics leading to a classification of the underlying cause. This understanding may enable specific diagnostic methods and appropriate interventions. We first review the different phenomena, providing an overview of their characteristics and their occurrence in sports and describing the affected sports and movements. We then analyze explanations for the yips, the most prominent phenomenon, and review the methodological approaches for diagnosing and treating it. Finally, we present and elaborate an action theoretical approach for diagnosing paradoxical performance and applying appropriate interventions.

scholarly journals Riemannian manifolds with local symmetry

2014 ◽  
Vol 06 (02) ◽  
pp. 211-236 ◽  
Author(s):  
Wouter van Limbeek
Keyword(s):  
Riemannian Manifolds ◽  
Local Symmetry ◽  
Universal Cover ◽  
Connected Components ◽  
Curved Manifolds ◽  
Locally Homogeneous ◽  
Simply Connected ◽  
Positively Curved ◽  
Aspherical Manifolds

We give a classification of many closed Riemannian manifolds M whose universal cover [Formula: see text] possesses a nontrivial amount of symmetry. More precisely, we consider closed Riemannian manifolds M such that [Formula: see text] has noncompact connected components. We prove that in many cases, such a manifold is as a fiber bundle over a locally homogeneous space. This is inspired by work of Eberlein (for non-positively curved manifolds) and Farb-Weinberger (for aspherical manifolds), and generalizes work of Frankel (for a semisimple group action). As an application, we characterize simply-connected Riemannian manifolds with both compact and finite volume noncompact quotients.

Almost complex manifolds with non-degenerate torsion

2017 ◽  
Vol 14 (03) ◽  
pp. 1750033
Author(s):  
Cristina Bozzetti ◽  
Costantino Medori
Keyword(s):  
Holomorphic Functions ◽  
Isotropy Subgroup ◽  
Text Structure ◽  
Complex Manifolds ◽  
Nijenhuis Tensor ◽  
Almost Complex Manifolds ◽  
Almost Complex ◽  
Locally Homogeneous ◽  
Infinitesimal Automorphisms

We show that almost complex manifolds [Formula: see text] of real dimension 4 for which the image of the Nijenhuis tensor forms a non-integrable bundle, called torsion bundle, admit a [Formula: see text]-structure locally, that is, a double absolute parallelism. In this way, the problem of equivalence for such almost complex manifolds can be solved; moreover, the classification of locally homogeneous manifold [Formula: see text] is explicitly given when the Lie algebra of its infinitesimal automorphisms is non-solvable (indeed reductive). It is also shown that the group of the automorphisms of [Formula: see text] is a Lie group of dimension less than or equal to 4, whose isotropy subgroup has at most two elements, and that there are not non-constant holomorphic functions on [Formula: see text].

scholarly journals A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ1= ρ2≠ ρ3

1993 ◽  
Vol 132 ◽  
pp. 1-36 ◽  
Author(s):  
Oldřich Kowalski
Keyword(s):  
Differential Geometry ◽  
Homogeneous Spaces ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Main Motivation ◽  
Locally Homogeneous ◽  
Riemannian Spaces

This paper has been motivated by various problems and results in differential geometry. The main motivation is the study of curvature homogeneous Riemannian spaces initiated in 1960 by I.M. Singer (see Section 9—Appendix for the precise definitions and references). Up to recently, only sporadic classes of examples have been known of curvature homogeneous spaces which are not locally homogeneous. For instance, isoparametric hypersurfaces in space forms give nice examples of nontrivial curvature homogeneous spaces (see [FKM]). To study the topography of curvature homogeneous spaces more systematically, it is natural to start with the dimension n = 3. The following results and problems have been particularly inspiring.

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