DOI: 10.15673/tmgc.v10i3-4.772 (ukr)
Authors:
- Евгений Владимирович Черевко
- Елена Евгеньевна Чепурная
Abstract | Full Text: 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.
Keywords:
- Ермітові многовиди
- конформно келерові мнговиди
- форма Лі
- конформно голоморфно-проективні перетворення