Remarks on natural differential operators with tensor fields

Josef Janyška

Address: Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

E-mail: janyska@math.muni.cz

Abstract: We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete situations.

AMSclassification: primary 53A32.

Keywords: tensor field, natural differential operator, Lie derivative, Yano-Ako operator.

DOI: 10.5817/AM2019-5-289