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