Instantons and multi-instantons in curvilinear coordinates

Instantons in regular and singular gauges and explicit multi-instanton Solu tions are generalized to curvilinear coordinates. Expressions can be simpli fied by fitting gauge orientation of the solutions to the vierbein. The gau ge transformation replaces eta-symbols used in Cartesian formalism by const ant xi-symbols and generates a compensating addition to the gauge potential of pseudoparticles. Typical examples (4-spherical, (2 + 2)- and (3 + 1)-cy lindrical coordinates) are studied explicitly. Effects of singularities of the compensating field on gauge dependent quantities are discussed. (C) 200 0 Elsevier Science B.V. All rights reserved.