A note on variational and metrizable connections

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

Alena Vanzurová¹ 

[1] Brno University of Technology

关键词: Helmholtz conditions;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

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.

【 授权许可】

Unknown