Integrability conditions for a certain class of nonlinear evolution equations and Kähler geometry

Differential Geometry and its Applications 5 (1995) 405 North- H oil and

405

Erratum

Integrability conditions for a certain class of nonlinear evolution equations and K/ihler geometry Diff. G e o m . A p p l . 1 ( 1 9 9 1 ) 3 2 7 - 3 4 4 E.M. Isaenko 1 Division o] Physics and Appl. Mathem., Vladimir State Technical University, Gorky ul. 87, 600026, Vladimir, Russia

There is an error in the proof of the Theorem 2.2. The correction concerns the "essential" components of the curvature tensor K and the form of the Ricci tensor R of the connection and consists in as follows. The mentioned components of K are Kit ~ and K~cd and the Ricci tensor is R = R + + R - , where

It can be proved that the Ricci tensor is J-invariant and symmetric, i.e., R = R + with P bah - = Rb~ (it is sufficient to investigate the compatibility conditions (2.6) and a~ObO~(r) =

ObO~O~(r),

a~ = o/o~ ~,

of the system (2.5)). The Theorem 2.2 holds, but it is preferably to replace the phrase %.. a) If the Ricci tensor R is non-singular as a bilinear form . . . " by " . . . Then the Ricci tensor R :is symmetric and J-invariant. a) If the Ricci tensor R is nongenerated as a symmetric bilinear form . . . " . The analogous replacement must be inserted into the Corrolary 2.3 and the Theorem 3.1. 1E-maih snk%[email protected]. 0926-2245/95/$09.50 @1995 Elsevier Science B.V. All rights reserved SSD[ 0926-2245 ( 95 ) 00024-0