Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 26, No. 2, pp. 383-396 (2010)

A note on variational and metrizable connections

Alena Vanzurová

Brno University of Technology

Abstract: We treat the problem of metrizability of a linear connection in the context of the inverse problem of the calculus of variations. Particularly, we show that in a 2-dimensional manifold endowed with a nowhere flat connection, Helmholtz conditions can be used to answer the metrizability problem in terms of components of the connection. In dim M>=3, the question is open.

Keywords: Manifold, connection, metric, calculus of variations, inverse problem, Helmholtz conditions

Classification (MSC2000): 53C05; 53C60

Full text of the article:


[Previous Article] [Next Article] [Contents of this Number]
© 2010–2011 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition