Transformations of compact locally conformally Kähler manifolds

Details Transformations of compact locally conformally Kähler manifolds Transformations of compact locally conformally Kähler manifolds

2000-11-08

arxiv.org/abs/math/0011050v1

Mathematics

Differential Geometry

22 pages. Latex, uses amscd, amsmath, amssymb, amsfonts packages

Scientific paper

We characterize compact locally conformally K\"ahler (l.c.K.) manifolds under the assumption of a purely conformal, holomorphic circle action. As an application, we determine the structure of the compact l.c.K. manifolds with parallel Lee form. We introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms preserving the specific $G$-structure of l.c.K. manifolds. Then we characterize the Hopf manifolds, up to holomorphic isometry, as compact l.c.K. manifolds admitting a certain closed LCR action of $\mathbb{C}^*$.

Affiliated with

Also associated with

No associations

Rating

Transformations of compact locally conformally Kähler manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Transformations of compact locally conformally Kähler manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transformations of compact locally conformally Kähler manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-125486