Natural first order Lagrangians for immersions

Jerzy J. Konderak

Annales Polonici Mathematici (1998)

  • Volume: 69, Issue: 3, page 207-215
  • ISSN: 0066-2216

Abstract

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We define natural first order Lagrangians for immersions of Riemannian manifolds and we prove a bijective correspondence between such Lagrangians and the symmetric functions on an open subset of m-dimensional Euclidean space.

How to cite

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Jerzy J. Konderak. "Natural first order Lagrangians for immersions." Annales Polonici Mathematici 69.3 (1998): 207-215. <http://eudml.org/doc/270492>.

@article{JerzyJ1998,
abstract = {We define natural first order Lagrangians for immersions of Riemannian manifolds and we prove a bijective correspondence between such Lagrangians and the symmetric functions on an open subset of m-dimensional Euclidean space.},
author = {Jerzy J. Konderak},
journal = {Annales Polonici Mathematici},
keywords = {natural Lagrangians; Riemannian immersions; jets},
language = {eng},
number = {3},
pages = {207-215},
title = {Natural first order Lagrangians for immersions},
url = {http://eudml.org/doc/270492},
volume = {69},
year = {1998},
}

TY - JOUR
AU - Jerzy J. Konderak
TI - Natural first order Lagrangians for immersions
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 3
SP - 207
EP - 215
AB - We define natural first order Lagrangians for immersions of Riemannian manifolds and we prove a bijective correspondence between such Lagrangians and the symmetric functions on an open subset of m-dimensional Euclidean space.
LA - eng
KW - natural Lagrangians; Riemannian immersions; jets
UR - http://eudml.org/doc/270492
ER -

References

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  1. [ES] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. Zbl0122.40102
  2. [G] G. Glaeser, Fonctions composées différentiables, Ann. of Math. (2) 77 (1963), 193-209. Zbl0106.31302
  3. [H] M. W. Hirsch, Differential Topology, Grad. Texts in Math. 33, Springer, New York, 1976. 
  4. [KMS] I. Kolar, P. W. Michor and J. Slovak, Natural Operations in Differential Geometry, Springer, New York, 1993. Zbl0782.53013
  5. [K] J. J. Konderak, On natural first order Lagrangians, Bull. London Math. Soc. 23 (1991), 169-174. Zbl0754.58008
  6. [M] P. W. Michor, Manifolds of Differentiable Mappings, Shiva Math. Ser., 1980. Zbl0433.58001
  7. [P₁] R. S. Palais, Foundations of Global Non-linear Analysis, Benjamin, New York, 1968. Zbl0164.11102
  8. [P₂] R. S. Palais, Applications of the symmetric criticality principle in mathematical physics and differential geometry, in: Proc. 1981 Symposium on Diff. Geometry and Diff. Equations, C. H. Gu (eds.), Science Press, Beijing, 1984, 247-302. Zbl0792.53079

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