aequationes mathematicae

, Volume 12, Issue 2–3, pp 232–241 | Cite as

Sufficiency conditions under which a lagrangian is an ordinary divergence

  • Gregory Walter Horndeski
Research Papers


An expression is derived for the variation of Lagrangians which are such that the set of admissible variables of variation is star-shaped. If such a Lagrangian leads to identically vanishing Euler-Lagrange expressions then it is shown that under suitable circumstances the Lagrangian in question must be an ordinary divergence. Furthermore, an expression is given for the ‘vector’ field which appears in this ordinary divergence.

AMS Primary Subject Classification


Secondary Subject Classifications

53A99 70D10 


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Copyright information

© Birkhäuser Verlag 1975

Authors and Affiliations

  • Gregory Walter Horndeski
    • 1
  1. 1.University of WaterlooWaterlooCanada

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