Extremal immersions and the extended frame bundle

Physics

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https://doi.org/10.1017/CBO9780511629334.015
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Extremal immersions and the extended frame bundle. / Hartley, D. H.; Tucker, Robin.
Geometry of low-dimensional manifolds: 1: gauge theory and algebraic surfaces. ed. / S. K. Donaldson; C. B. Thomas. Cambridge: Cambridge University Press, 1991. p. 207-230 (London Mathematical Society Lecture Note Series; No. 150).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Harvard

Hartley, DH & Tucker, R 1991, Extremal immersions and the extended frame bundle. in SK Donaldson & CB Thomas (eds), Geometry of low-dimensional manifolds: 1: gauge theory and algebraic surfaces. London Mathematical Society Lecture Note Series, no. 150, Cambridge University Press, Cambridge, pp. 207-230. https://doi.org/10.1017/CBO9780511629334.015

APA

Hartley, D. H., & Tucker, R. (1991). Extremal immersions and the extended frame bundle. In S. K. Donaldson, & C. B. Thomas (Eds.), Geometry of low-dimensional manifolds: 1: gauge theory and algebraic surfaces (pp. 207-230). (London Mathematical Society Lecture Note Series; No. 150). Cambridge University Press. https://doi.org/10.1017/CBO9780511629334.015

Vancouver

Hartley DH, Tucker R. Extremal immersions and the extended frame bundle. In Donaldson SK, Thomas CB, editors, Geometry of low-dimensional manifolds: 1: gauge theory and algebraic surfaces. Cambridge: Cambridge University Press. 1991. p. 207-230. (London Mathematical Society Lecture Note Series; 150). doi: 10.1017/CBO9780511629334.015

Author

Hartley, D. H. ; Tucker, Robin. / Extremal immersions and the extended frame bundle. Geometry of low-dimensional manifolds: 1: gauge theory and algebraic surfaces. editor / S. K. Donaldson ; C. B. Thomas. Cambridge : Cambridge University Press, 1991. pp. 207-230 (London Mathematical Society Lecture Note Series; 150).

Bibtex

@inbook{ef2fa037a6814750a6d1adebf8795255,

title = "Extremal immersions and the extended frame bundle",

abstract = "We present a computationally powerful formulation of variational problems that depend on the extrinsic and intrinsic geometry of immersions into a manifold. The approach is based on a lift of the action integral to a larger space and proceeds by systematically constraining the variations to preserve the foliation of a Pfaffian system on an extended frame bundle. Explicit Euler-Lagrange equations are computed for a very general class of Lagrangians and the method illustrated with examples relevant to recent developments in theoretical physics. The method provides a means of determining spatial boundary conditions for immersions with boundary and enables a construction to be made of constants of the motion in terms of Euler- Lagrange solutions and admissible symmetry vectors.",

author = "Hartley, {D. H.} and Robin Tucker",

year = "1991",

doi = "10.1017/CBO9780511629334.015",

language = "English",

isbn = "9780521399784",

series = "London Mathematical Society Lecture Note Series",

publisher = "Cambridge University Press",

number = "150",

pages = "207--230",

editor = "Donaldson, {S. K.} and Thomas, {C. B.}",

booktitle = "Geometry of low-dimensional manifolds",

}

RIS

TY - CHAP

T1 - Extremal immersions and the extended frame bundle

AU - Hartley, D. H.

AU - Tucker, Robin

PY - 1991

Y1 - 1991

N2 - We present a computationally powerful formulation of variational problems that depend on the extrinsic and intrinsic geometry of immersions into a manifold. The approach is based on a lift of the action integral to a larger space and proceeds by systematically constraining the variations to preserve the foliation of a Pfaffian system on an extended frame bundle. Explicit Euler-Lagrange equations are computed for a very general class of Lagrangians and the method illustrated with examples relevant to recent developments in theoretical physics. The method provides a means of determining spatial boundary conditions for immersions with boundary and enables a construction to be made of constants of the motion in terms of Euler- Lagrange solutions and admissible symmetry vectors.

AB - We present a computationally powerful formulation of variational problems that depend on the extrinsic and intrinsic geometry of immersions into a manifold. The approach is based on a lift of the action integral to a larger space and proceeds by systematically constraining the variations to preserve the foliation of a Pfaffian system on an extended frame bundle. Explicit Euler-Lagrange equations are computed for a very general class of Lagrangians and the method illustrated with examples relevant to recent developments in theoretical physics. The method provides a means of determining spatial boundary conditions for immersions with boundary and enables a construction to be made of constants of the motion in terms of Euler- Lagrange solutions and admissible symmetry vectors.

U2 - 10.1017/CBO9780511629334.015

DO - 10.1017/CBO9780511629334.015

M3 - Chapter

SN - 9780521399784

T3 - London Mathematical Society Lecture Note Series

SP - 207

EP - 230

BT - Geometry of low-dimensional manifolds

A2 - Donaldson, S. K.

A2 - Thomas, C. B.

PB - Cambridge University Press

CY - Cambridge

ER -

Research

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