An integral invariant from the view point of locally conformally Kähler geometry

Details An integral invariant from the view point of locally conformally Kähler geometry An integral invariant from the view point of locally conformally Kähler geometry

2011-05-24

arxiv.org/abs/1105.4774v1

Mathematics

Differential Geometry

12 pages

Scientific paper

In this paper we study an integral invariant which obstructs the existence on a compact complex manifold of a volume form with the determinant of its Ricci form proportional to itself, in particular obstructs the existence of a K\"ahler-Einstein metric, and has been studied since 1980's. We study this invariant from the view point of locally conformally K\"ahler geometry. We first see that we can define an integral invariant for coverings of compact complex manifolds with automorphic volume forms. This situation typically occurs for locally conformally K\"ahler manifolds. Secondly, we see that this invariant coincides with the former one. We also show that the invariant vanishes for any compact Vaisman manifolds.

Affiliated with

Also associated with

No associations

Rating

An integral invariant from the view point of locally conformally Kähler geometry 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 An integral invariant from the view point of locally conformally Kähler geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An integral invariant from the view point of locally conformally Kähler geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-515924