Homogeneous variational problems: a minicourse

David J. Saunders

Communications in Mathematics (2011)

  • Volume: 19, Issue: 2, page 91-128
  • ISSN: 1804-1388

Abstract

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A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension $m$. In this minicourse we discuss these problems from a geometric point of view.

How to cite

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Saunders, David J.. "Homogeneous variational problems: a minicourse." Communications in Mathematics 19.2 (2011): 91-128. <http://eudml.org/doc/246199>.

@article{Saunders2011,
abstract = {A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension $m$. In this minicourse we discuss these problems from a geometric point of view.},
author = {Saunders, David J.},
journal = {Communications in Mathematics},
keywords = {calculus of variations; parametric problems},
language = {eng},
number = {2},
pages = {91-128},
publisher = {University of Ostrava},
title = {Homogeneous variational problems: a minicourse},
url = {http://eudml.org/doc/246199},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Saunders, David J.
TI - Homogeneous variational problems: a minicourse
JO - Communications in Mathematics
PY - 2011
PB - University of Ostrava
VL - 19
IS - 2
SP - 91
EP - 128
AB - A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension $m$. In this minicourse we discuss these problems from a geometric point of view.
LA - eng
KW - calculus of variations; parametric problems
UR - http://eudml.org/doc/246199
ER -

References

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  1. Crampin, M., Saunders, D.J., 10.1007/s10587-009-0044-0, Czech Math. J. 59 (3) 2009 741-758 (2009) Zbl1224.58012MR2545653DOI10.1007/s10587-009-0044-0
  2. Giaquinta, M., Hildebrandt, S., Calculus of Variations II, Springer 1996 (1996) MR1385926
  3. Kolář, I., Michor, P.W., Slovák, J., Natural Operations in Differential Geometry, Springer 1993 (1993) MR1202431
  4. Rund, H., The Hamilton-Jacobi Equation in the Calculus of Variations, Krieger 1973 (1973) 
  5. Saunders, D.J., Homogeneous variational complexes and bicomplexes, J. Geom. Phys. 59 2009 727-739 (2009) Zbl1168.58006MR2510165
  6. Saunders, D.J., Some geometric aspects of the calculus of variations in several independent variables, Comm. Math. 18 (1) 2010 3-19 (2010) Zbl1235.58014MR2848502

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