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Relevant bibliographies by topics / Tangent bundle of Lie groups

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Academic literature on the topic 'Tangent bundle of Lie groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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Journal articles on the topic "Tangent bundle of Lie groups"

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Balan, Vladimir, Maido Rahula, and Nicoleta Voicu. "Iterative calculus on tangent floors." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 1 (2016): 121–52. http://dx.doi.org/10.1515/auom-2016-0007.

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AbstractTangent fibrations generate a “multi-floored tower”, while raising from one of its floors to the next one, one practically reiterates the previously performed actions. In this way, the "tower" admits a ladder-shaped structure. Raising to the first floors suffices for iteratively performing the subsequent steps. The paper mainly studies the tangent functor. We describe the structure of multiple vector bundle which naturally appears on the floors, tangent maps, sector-forms, the lift of vector fields to upper floors. Further, we show how tangent groups of Lie groups lead to gauge theory,

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SEIFIPOUR, Davood, and Esmaeil PEYGHAN. "Some properties of Riemannian geometry of the tangent bundle of Lie groups." TURKISH JOURNAL OF MATHEMATICS 43, no. 6 (2019): 2842–64. http://dx.doi.org/10.3906/mat-1812-94.

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Asgari, Farhad, and Hamid Reza Salimi Moghaddam. "Left invariant Randers metrics of Berwald type on tangent Lie groups." International Journal of Geometric Methods in Modern Physics 15, no. 01 (2017): 1850015. http://dx.doi.org/10.1142/s0219887818500159.

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Let [Formula: see text] be a Lie group equipped with a left invariant Randers metric of Berward type [Formula: see text], with underlying left invariant Riemannian metric [Formula: see text]. Suppose that [Formula: see text] and [Formula: see text] are lifted Randers and Riemannian metrics arising from [Formula: see text] and [Formula: see text] on the tangent Lie group [Formula: see text] by vertical and complete lifts. In this paper, we study the relations between the flag curvature of the Randers manifold [Formula: see text] and the sectional curvature of the Riemannian manifold [Formula: s

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Ivancevic, V., and C. E. M. Pearce. "Topological duality in humanoid robot dynamics." ANZIAM Journal 43, no. 2 (2001): 183–94. http://dx.doi.org/10.1017/s144618110001302x.

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AbstractA humanoid robot system may be viewed as a collection of segments coupled at rotational joints which geometrically represent constrained rotational Lie groups. This allows a study of the dynamics of the motion of a humanoid robot. Several formulations are possible. In this paper, dual invariant topological structures are constructed and analyzed on the finite-dimensional manifolds associated with the humanoid motion. Both cohomology and homology structures are examined on the tangent (Lagrangian) as well as on the cotangent (Hamiltonian) bundles on the manifold of the humanoid motion c

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Machida, Yoshinori, and Hajime Sato. "Twistor theory of manifolds with Grassmannian structures." Nagoya Mathematical Journal 160 (2000): 17–102. http://dx.doi.org/10.1017/s0027763000007698.

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AbstractAs a generalization of the conformal structure of type (2, 2), we study Grassmannian structures of type (n, m) forn, m≥ 2. We develop their twistor theory by considering the complete integrability of the associated null distributions. The integrability corresponds to global solutions of the geometric structures.A Grassmannian structure of type (n, m) on a manifoldMis, by definition, an isomorphism from the tangent bundleTMofMto the tensor productV ⊗ Wof two vector bundlesVandWwith ranknandmoverMrespectively. Because of the tensor product structure, we have two null plane bundles with f

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IVANCEVIC, VLADIMIR G., and TIJANA T. IVANCEVIC. "HUMAN VERSUS HUMANOID ROBOT BIODYNAMICS." International Journal of Humanoid Robotics 05, no. 04 (2008): 699–713. http://dx.doi.org/10.1142/s0219843608001595.

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In this paper we compare and contrast modern dynamical methodologies common to both humanoid robotics and human biomechanics. While the humanoid robot's motion is defined on the system of constrained rotational Lie groups SO(3) acting in all major robot joints, human motion is defined on the corresponding system of constrained Euclidean groups SE(3) of the full (rotational + translational) rigid motions acting in all synovial human joints. In both cases the smooth configuration manifolds, Q rob and Q hum , respectively, can be constructed. The autonomous Lagrangian dynamics are developed on th

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Bekar, Murat, and Yusuf Yayli. "Lie Algebra of Unit Tangent Bundle." Advances in Applied Clifford Algebras 27, no. 2 (2016): 965–75. http://dx.doi.org/10.1007/s00006-016-0670-1.

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Blair, David E. "A Survey of Riemannian Contact Geometry." Complex Manifolds 6, no. 1 (2019): 31–64. http://dx.doi.org/10.1515/coma-2019-0002.

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AbstractThis survey is a presentation of the five lectures on Riemannian contact geometry that the author gave at the conference “RIEMain in Contact”, 18-22 June 2018 in Cagliari, Sardinia. The author was particularly pleased to be asked to give this presentation and appreciated the organizers’ kindness in dedicating the conference to him. Georges Reeb once made the comment that the mere existence of a contact form on a manifold should in some sense “tighten up” the manifold. The statement seemed quite pertinent for a conference that brought together both geometers and topologists working on c

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CRASMAREANU, MIRCEA. "DIRAC STRUCTURES FROM LIE INTEGRABILITY." International Journal of Geometric Methods in Modern Physics 09, no. 04 (2012): 1220005. http://dx.doi.org/10.1142/s0219887812200058.

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We prove that a pair (F = vector sub-bundle of TM, its annihilator) yields an almost Dirac structure which is Dirac if and only if F is Lie integrable. Then a flat Ehresmann connection on a fiber bundle ξ yields two complementary, but not orthogonally, Dirac structures on the total space M of ξ. These Dirac structures are also Lagrangian sub-bundles with respect to the natural almost symplectic structure of the big tangent bundle of M. The tangent bundle in Riemannian geometry is discussed as particular case and the 3-dimensional Heisenberg space is illustrated as example. More generally, we s

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Vulcu, Vlad-Augustin. "Dirac Structures on Banach Lie Algebroids." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 3 (2014): 219–28. http://dx.doi.org/10.2478/auom-2014-0060.

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Abstract In the original definition due to A. Weinstein and T. Courant a Dirac structure is a subbundle of the big tangent bundle T M ⊕ T* M that is equal to its ortho-complement with respect to the so-called neutral metric on the big tangent bundle. In this paper, instead of the big tangent bundle we consider the vector bundle E ⊕ E*, where E is a Banach Lie algebroid and E* its dual. Recall that E* is not in general a Lie algebroid. We define a bilinear and symmetric form on the vector bundle E ⊕ E* and say that a subbundle of it is a Dirac structure if it is equal with its orthocomplement.

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Dissertations / Theses on the topic "Tangent bundle of Lie groups"

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Hindeleh, Firas Y. "Tangent and Cotangent Bundles, Automorphism Groups and Representations of Lie Groups." University of Toledo / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1153933389.

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Hindeleh, Firas. "Tangent and cotangent bundles automorphism groups and representations of Lie groups /." See Full Text at OhioLINK ETD Center (Requires Adobe Acrobat Reader for viewing), 2006. http://www.ohiolink.edu/etd/view.cgi?acc_num=toledo1153933389.

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Thesis (Ph.D.)--University of Toledo, 2006.<br>Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 79-82.

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Eddy, Scott M. "Lie Groups and Lie Algebras." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1320152161.

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Mortada, Amina. "Roulement de variétés différentielles de dimensions quelconques." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112324/document.

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Nous étudions dans cette thèse le roulement sans glissement et sans pivotement de deux variétés lisses M et Ṁ l'une sur l'autre de dimensions et n et ṅ respectivement. L'objectif principal est de chercher des conditions nécessaires et suffisantes de la commandabilité du système commandé défini par le roulement. Dans le premier chapitre, on présente les motivations et le plan de la thèse ainsi les notations utilisées le long des chapitres. Dans le deuxième chapitre, on caractérise l'espace d'état du roulement quand M et Ṁ sont des variétés Riemanniennes lorsque n n'est pas nécessairement égal à

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Ewert, Eske Ellen. "Index theory and groupoids for filtered manifolds." Doctoral thesis, 2020. http://hdl.handle.net/21.11130/00-1735-0000-0005-152D-2.

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Books on the topic "Tangent bundle of Lie groups"

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Mann, Peter. Linear Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0037.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, fo

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Mann, Peter. Differential Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0038.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree ofmathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactlywhat is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, form

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Mann, Peter. Symmetries & Lagrangian-Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0011.

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This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s theorem’, after Amalie ‘Emmy’ Noether, who first discovered it in 1918. The chapter starts off by discussing Noether’s theorem and symmetry transformations in Lagrangian mechanics in detail. It then moves on to gauge theory and surface terms in the action before isotropic symmetries. continuous symmetry, conserved quantities, conjugate momentum, cyclic coordinates, Hessian condition and discrete symmetries are disc

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Canarutto, Daniel. Gauge Field Theory in Natural Geometric Language. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198861492.001.0001.

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This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connect

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Book chapters on the topic "Tangent bundle of Lie groups"

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Onishchik, A. L. "A Spectral Sequence for the Tangent Sheaf Cohomology of a Supermanifold." In Lie Groups and Lie Algebras. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5258-7_13.

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Gallier, Jean, and Jocelyn Quaintance. "Manifolds, Tangent Spaces, Cotangent Spaces, and Submanifolds." In Differential Geometry and Lie Groups. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46040-2_8.

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Neeb, Karl-Hermann. "Lie Groups of Bundle Automorphisms and Their Extensions." In Developments and Trends in Infinite-Dimensional Lie Theory. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4741-4_9.

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Marion, Jean. "Construction of Quasi Invariant Probability Measures on Some Current Groups of Continuous Sections of a Bundle of Compact Semisimple Lie Groups." In Probability Measures on Groups X. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-2364-6_20.

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Tu, Loring W. "Fundamental Vector Fields." In Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0011.

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This chapter addresses fundamental vector fields. The concept of a connection on a principal bundle is essential in the construction of the Cartan model. To define a connection on a principal bundle, one first needs to define the fundamental vector fields. When a Lie group acts smoothly on a manifold, every element of the Lie algebra of the Lie group generates a vector field on the manifold called a fundamental vector field. On a principal bundle, the fundamental vectors are precisely the vertical tangent vectors. In general, there is a relation between zeros of fundamental vector fields and fixed points of the group action. Unless specified otherwise (such as on a principal bundle), a group action is assumed to be a left action.

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Tu, Loring W. "The Maurer–Cartan Form." In Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0015.

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This chapter illustrates the Maurer-Cartan form. On every Lie group G with Lie algebra g, there is a unique canonically defined left-invariant g-valued 1-form called the Maurer-Cartan form. The chapter describes the Maurer-Cartan form and the equation it satisfies, the Maurer-Cartan equation. The Maurer-Cartan form allows one to define a connection on the product bundle M × G → M for any manifold M. The Lie algebra g of a Lie group G is defined to be the tangent space at the identity. One will often identify the two vector spaces and think of elements of g as left-invariant vector fields on G.

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"Tangent spaces. Separability." In Lectures on Lie Groups and Lie Algebras. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9781139172882.030.

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"Bundle Properties of a Discriminantal Configuration." In Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/9789812798237_0006.

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Conference papers on the topic "Tangent bundle of Lie groups"

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Seo, Dongeun, and Morad Nazari. "Rigid Body Adaptive Stabilization on the Tangent Bundle of the LIE Groups." In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-0653.

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Izadi, Maziar, Jan Bohn, Daero Lee, Amit K. Sanyal, Eric Butcher, and Daniel J. Scheeres. "A Nonlinear Observer Design for a Rigid Body in the Proximity of a Spherical Asteroid." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4085.

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We consider an observer design for a spacecraft modeled as a rigid body in the proximity of an asteroid. The nonlinear observer is constructed on the nonlinear state space of motion of a rigid body, which is the tangent bundle of the Lie group of rigid body motions in three-dimensional Euclidean space. The framework of geometric mechanics is used for the observer design. States of motion of the spacecraft are estimated based on state measurements. In addition, the observer designed can also estimate the gravity parameter of the asteroid, assuming the asteroid to have a spherically symmetric ma

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Jinhui Chao and Fang Xing Li. "A surface model based on a fibre bundle of 1-parameter groups of Hamiltonian Lie algebra." In 2005 International Conference on Image Processing. IEEE, 2005. http://dx.doi.org/10.1109/icip.2005.1529927.

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Bonsignorio, Fabio. "On the Stochastic Stability and Observability of Controlled Serial Kinematic Chains." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-25131.

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In this paper the stability and observability of a controlled serial kinematic chain are analyzed with reference to a characterization of observability and stability for a stochastic system grounded in the application of Shannon theory to controlled systems. This approach was proposed in 2004 by H. Touchette and S. Lloyd. In particular it is analyzed in depth the case in which errors on the joints follow (concentrated) Gaussian distributions. In this case the property of Lie Groups (and related tangent space Lie algebra), studied from G. Chirikjian et al., allow to carry out the study of stoch

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Reports on the topic "Tangent bundle of Lie groups"

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Boumaiza, Mohamed. Poisson-Lie Structure on the Tangent Bundle of a Poisson-Lie Group and Poisson Action Lifting. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-4-2005-1-18.

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