scholarly journals On Some Transverse Geometrical Structures of Lifted Foliation to Its Conormal Bundle

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Cristian Ida ◽  
Alexandru Oană
Keyword(s):  
Normal Bundle ◽  
Contact Structure ◽  
Geometrical Structures ◽  
Liouville Distribution ◽  
Conormal Bundle

We consider the lift of a foliation to its conormal bundle and some transverse geometrical structures associated with this foliation are studied. We introduce a good vertical connection on the conormal bundle and, moreover, if the conormal bundle is endowed with a transversal Cartan metric, we obtain that the lifted foliation to its conormal bundle is a Riemannian one. Also, some transversally framedf(3, ε)-structures of corank 2 on the normal bundle of lifted foliation to its conormal bundle are introduced and an almost (para)contact structure on a transverse Liouville distribution is obtained.

STATIONARY DISCS AND GEOMETRY OF CR MANIFOLDS OF CODIMENSION TWO

2001 ◽  
Vol 12 (08) ◽  
pp. 877-890 ◽  
Author(s):  
A. SUKHOV ◽  
A. TUMANOV
Keyword(s):  
Contact Structure ◽  
Cr Manifolds ◽  
Codimension Two ◽  
Strictly Convex ◽  
Cr Structure ◽  
Conormal Bundle ◽  
Convex Hypersurfaces

We give a construction of stationary discs and the indicatrix for manifolds of higher codimension which is a partial analog of L. Lempert's theory of stationary discs for strictly convex hypersurfaces. This leads to new invariants of the CR structure in higher codimension linked with the contact structure of the conormal bundle.

scholarly journals Contact geometry for simple thermodynamical systems with friction

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200244
Author(s):  
Alexandre Anahory Simoes ◽  
Manuel de León ◽  
Manuel Lainz Valcázar ◽  
David Martín de Diego
Keyword(s):  
Contact Structure ◽  
Evolution Equations ◽  
Gradient Methods ◽  
Important Class ◽  
Geometrical Structures ◽  
Laws Of Thermodynamics ◽  
Qualitative Dynamics ◽  
Isolated Systems ◽  
Jacobi Structure

By means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamical systems with friction, a simple but important class of thermodynamical systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and non-decreasing total entropy, respectively. We completely clarify its qualitative dynamics, the underlying geometrical structures and we also show how to apply discrete gradient methods to numerically integrate the evolution equations for these systems.

Remarks on infinitesimal symmetries of geometrical structures of the classical phase space of general relativistic test particle

2015 ◽  
Vol 12 (08) ◽  
pp. 1560020 ◽  
Author(s):  
Josef Janyška
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Test Particle ◽  
Contact Structure ◽  
Jet Space ◽  
Geometrical Structures ◽  
Lorentzian Metric ◽  
Dimensional Phase Space ◽  
General Relativistic ◽  
Classical Phase Space

The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric and an electromagnetic field define the joined almost-cosymplectic-contact structure on the odd-dimensional phase space. In this paper, we study infinitesimal symmetries (ISs) of this phase structure. We prove that there are no hidden ISs.

Autonomous Geometrical Mechanics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Contact Structure ◽  
Invariant Tori ◽  
Time Dependent ◽  
Contact Structures ◽  
Natural Setting ◽  
Adiabatic Invariance ◽  
Jet Bundle ◽  
Integrability Theorem ◽  
Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

scholarly journals Quaternionic contact 4n + 3-manifolds and their 4n-quotients

2021 ◽  
Author(s):  
Yoshinobu Kamishima
Keyword(s):  
Scalar Curvature ◽  
Lie Group ◽  
Contact Structure ◽  
Einstein Manifolds ◽  
Hermitian Metrics ◽  
Kähler Metric ◽  
Formula One ◽  
Quaternion Space ◽  
Kahler Metric ◽  
Do So

AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$ ( g a , { J α } α = 1 3 ) on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$ H n one of which, say $$(g_a,J_1)$$ ( g a , J 1 ) is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$ M to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$ R 3 .

Anyon Networks from Geometric Models of Matter

2021 ◽  
Author(s):  
Michael Atiyah ◽  
Matilde Marcolli
Keyword(s):  
Normal Bundle ◽  
Present Form ◽  
Joint Work ◽  
Geometric Models ◽  
Tensor Networks

Abstract This paper, completed in its present form by the second author after the first author passed away in 2019, describes an intended continuation of the previous joint work on anyons in geometric models of matter. This part outlines a construction of anyon tensor networks based on four-dimensional orbifold geometries and braid representations associated with surface-braids defined by multisections of the orbifold normal bundle of the surface of orbifold points.

scholarly journals Analysis of Occlusion Effects for Map-Based Self-Localization in Urban Areas

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5196
Author(s):  
Yuki Endo ◽  
Ehsan Javanmardi ◽  
Shunsuke Kamijo
Keyword(s):  
Urban Areas ◽  
Structural Information ◽  
Average Error ◽  
High Definition ◽  
Geometrical Structures ◽  
Real Environment ◽  
Surrounding Environment ◽  
Localization Errors ◽  
Stable Estimation ◽  
High Level

A high-definition (HD) map provides structural information for map-based self-localization, enabling stable estimation in real environments. In urban areas, there are many obstacles, such as buses, that occlude sensor observations, resulting in self-localization errors. However, most of the existing HD map-based self-localization evaluations do not consider sudden significant errors due to obstacles. Instead, they evaluate this in terms of average error over estimated trajectories in an environment with few occlusions. This study evaluated the effects of self-localization estimation on occlusion with synthetically generated obstacles in a real environment. Various patterns of synthetic occlusion enabled the analyses of the effects of self-localization error from various angles. Our experiments showed various characteristics that locations susceptible to obstacles have. For example, we found that occlusion in intersections tends to increase self-localization errors. In addition, we analyzed the geometrical structures of a surrounding environment in high-level error cases and low-level error cases with occlusions. As a result, we suggested the concept that the real environment should have to achieve robust self-localization under occlusion conditions.

scholarly journals The Legendrian knot complement problem

2018 ◽  
Vol 27 (14) ◽  
pp. 1850067 ◽  
Author(s):  
Marc Kegel
Keyword(s):  
Contact Structure ◽  
Legendrian Knot ◽  
Tight Contact ◽  
Legendrian Links ◽  
User Friendly ◽  
The Way

We prove that every Legendrian knot in the tight contact structure of the [Formula: see text]-sphere is determined by the contactomorphism type of its exterior. Moreover, by giving counterexamples we show this to be not true for Legendrian links in the tight [Formula: see text]-sphere. On the way a new user-friendly formula for computing the Thurston–Bennequin invariant of a Legendrian knot in a surgery diagram is given.

scholarly journals Doping the Buckminsterfullerene by Substitution: Density Functional Theory Studies of C59X (X = B, N, Al, Si, P, Ga, Ge, and As)

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongcun Bai ◽  
Wenxin Ji ◽  
Xiangyu Liu ◽  
Liqiong Wang ◽  
Nini Yuan ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Physical Properties ◽  
Density Functional ◽  
Dielectric Constants ◽  
Geometrical Structures ◽  
Functional Theory ◽  
Relative Stabilities ◽  
As Doping ◽  
Quantum Chemistry Calculations ◽  
Heteroatom Substitution

The heterofullerenes C59X (X = B, N, Al, Si, P, Ga, Ge, and As) were investigated by quantum chemistry calculations based on density functional theory. These hybrid cages can be seen as doping the buckminsterfullerene by heteroatom substitution. The geometrical structures, relative stabilities, electronic properties, vibrational frequencies, dielectric constants, and aromaticities of the doped cages were studied systemically and compared with those of the pristine C60cage. It is found that the doped cages with different heteroatoms exhibit various electronic, vibrational, and aromatic properties. These results imply the possibility to modulate the physical properties of these fullerene-based materials by tuning substitution elements.

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