scholarly journals A Tangent Bundle Theory for Visual Curve Completion

2012 ◽  
Vol 34 (7) ◽  
pp. 1263-1280 ◽  
Author(s):  
Guy Ben-Yosef ◽  
Ohad Ben-Shahar
Keyword(s):  
Tangent Bundle ◽  
Bundle Theory ◽  
Curve Completion

Golden Riemannian structures on the tangent bundle with g-natural metrics

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2543-2554
Author(s):  
E. Peyghan ◽  
F. Firuzi ◽  
U.C. De
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Riemannian Metric

Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

Families over a base with a birationally nef tangent bundle

1997 ◽  
Vol 308 (2) ◽  
pp. 347-359 ◽  
Author(s):  
Sándor J. Kovács
Keyword(s):  
Tangent Bundle

scholarly journals Vortices over Riemann surfaces and dominated splittings

2021 ◽  
pp. 1-26
Author(s):  
THOMAS METTLER ◽  
GABRIEL P. PATERNAIN
Keyword(s):  
Euler Characteristic ◽  
Tangent Bundle ◽  
Riemann Surfaces ◽  
Dominated Splitting ◽  
Vortex Equations ◽  
Special Cases ◽  
Unit Tangent Bundle ◽  
Anosov Flows

Abstract We associate a flow $\phi $ with a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $\phi $ always admits a dominated splitting and identify special cases in which $\phi $ is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of $(M,g)$ .

scholarly journals $$ \mathcal{N} $$ = 2 consistent truncations from wrapped M5-branes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Davide Cassani ◽  
Grégoire Josse ◽  
Michela Petrini ◽  
Daniel Waldram
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Tangent Bundle ◽  
Dimensional Manifold ◽  
Five Dimensions ◽  
Intrinsic Torsion ◽  
Consistent Truncations

Abstract We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold M, preserving minimal $$ \mathcal{N} $$ N = 2 supersymmetry in five dimensions. These are based on GS ⊆ USp(6) structures for the generalised E6(6) tangent bundle on M, such that the intrinsic torsion is a constant GS singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS5×wM solutions arising from M5-branes wrapped on a Riemann surface. The generalised U(1) structure associated with the $$ \mathcal{N} $$ N = 2 solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and SO(3) × U(1) × ℝ gauge group. The generalised structure associated with “BBBW” solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.

scholarly journals The Bundle Theory Approach to Relational Quantum Mechanics

2021 ◽  
Vol 51 (1) ◽  
Author(s):  
Andrea Oldofredi
Keyword(s):  
Quantum Mechanics ◽  
David Hume ◽  
Structural Realism ◽  
Bundle Theory ◽  
Theory Approach ◽  
Relational Quantum Mechanics ◽  
Essential Idea ◽  
Mereological Fusion ◽  
Metaphysical Interpretation ◽  
Aristotelian Tradition

AbstractThe present essay provides a new metaphysical interpretation of Relational Quantum Mechanics (RQM) in terms of mereological bundle theory. The essential idea is to claim that a physical system in RQM can be defined as a mereological fusion of properties whose values may vary for different observers. Abandoning the Aristotelian tradition centered on the notion of substance, I claim that RQM embraces an ontology of properties that finds its roots in the heritage of David Hume. To this regard, defining what kind of concrete physical objects populate the world according to RQM, I argue that this theoretical framework can be made compatible with (i) a property-oriented ontology, in which the notion of object can be easily defined, and (ii) moderate structural realism, a philosophical position where relations and relata are both fundamental. Finally, I conclude that under this reading relational quantum mechanics should be included among the full-fledged realist interpretations of quantum theory.

Some Properties of Symplectic Manifolds S on the Projective Tangent Bundle PTM

2011 ◽  
Vol 187 ◽  
pp. 483-486
Author(s):  
Yong He ◽  
Xiao Ying Lu ◽  
Wei Na Lu
Keyword(s):  
Vector Field ◽  
Symplectic Manifold ◽  
Tangent Bundle ◽  
Fiber Bundle ◽  
Symplectic Manifolds ◽  
Lie Derivative ◽  
The Relationship

In this paper, we show the relationship between 2-form of the two projective tangent bundle and the relationship between 2-form on projective tangent bundle and 1-form on by using the theory of fiber bundle and the properties of symplectic manifold of the projective tangent bundle . Moreover, we derived a simpler formula of Lie derivative of a special vector field, which is on the projective tangent bundle.

scholarly journals EXTENDED ABSOLUTE PARALLELISM GEOMETRY

2008 ◽  
Vol 05 (07) ◽  
pp. 1109-1135 ◽  
Author(s):  
NABIL. L. YOUSSEF ◽  
A. M. SID-AHMED
Keyword(s):  
Tangent Bundle ◽  
Special Form ◽  
Vector Fields ◽  
A Priori ◽  
Building Blocks ◽  
Absolute Parallelism ◽  
Linearly Independent ◽  
Geometric Objects ◽  
Directional Argument ◽  
Curvature Tensors

In this paper, we study Absolute Parallelism (AP-) geometry on the tangent bundle TM of a manifold M. Accordingly, all geometric objects defined in this geometry are not only functions of the positional argument x, but also depend on the directional argument y. Moreover, many new geometric objects, which have no counterpart in the classical AP-geometry, emerge in this different framework. We refer to such a geometry as an Extended Absolute Parallelism (EAP-) geometry. The building blocks of the EAP-geometry are a nonlinear connection (assumed given a priori) and 2n linearly independent vector fields (of special form) defined globally on TM defining the parallelization. Four different d-connections are used to explore the properties of this geometry. Simple and compact formulae for the curvature tensors and the W-tensors of the four defined d-connections are obtained, expressed in terms of the torsion and the contortion tensors of the EAP-space. Further conditions are imposed on the canonical d-connection assuming that it is of Cartan type (resp. Berwald type). Important consequences of these assumptions are investigated. Finally, a special form of the canonical d-connection is studied under which the classical AP-geometry is recovered naturally from the EAP-geometry. Physical aspects of some of the geometric objects investigated are pointed out and possible physical implications of the EAP-space are discussed, including an outline of a generalized field theory on the tangent bundle TM of M.

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