Інваріантні об'єкти конформно голоморфно-проективних перетворень ЛКК-многовидів

Abstract

The article is devoted to the problem of holomorphically projective transformations of locally conformal Kaehler manifolds. it's worth to be noted,  that J. Mikes and Z. Radulovich have proved that a locally conformal Kaehler manifold  does not admit finite nontrivial holomorphically projective mappings for  a Levi-Civita connection. Earlier we had proved that  a locally conformal Kaehler manifold  also does not admit nontrivial infinitesimal holomorphically projective transformations for a Levi-Civita connection. But since the Weyl connection defined by Lee form on a locally conformal Kaehler manifold  is F-connection, hence for the connection   nontrivial infinitesimal holomorphically projective transformations  are admitted. Then we rewrote the system of partial differential equations for the Levi-Civita connection. So we introduced  so called infinitesimal conformal holomorphically projective transformations. We have got the necessary and sufficient  conditions in order that the a locally conformal Kaehler manifold  admits a group of infinitesimal conformal holomorphically projective transformations. Also we have calculated  the number of parameters which the group depend on. We have got invariants, i. e. a tensor and a non-tensor which are preserved by the transformations. And finally, we have proved that  a vector field which generates infinitesimal conformal holomorphically projective transformations of a compact locally conformal Kaehler manifold  is contravariant almost analytic.