Vanishing theorems for locally conformal hyperkaehler manifolds

Details Vanishing theorems for locally conformal hyperkaehler manifolds Vanishing theorems for locally conformal hyperkaehler manifolds

2003-02-19

arxiv.org/abs/math/0302219v4

Proc. of Steklov Institute, vol. 246, 2004, pp. 54-79

Mathematics

Differential Geometry

41 pages. Reference added, typing errors corrected

Scientific paper

Let M be a compact locally conformal hyperkaehler manifold. We prove a version of Kodaira-Nakano vanishing theorem for M. This is used to show that M admits no holomorphic differential forms, and the cohomology of the structure sheaf $H^i(O_M)$ vanishes for i>1. We also prove that the first Betti number of M is 1. This leads to a structure theorem for locally conformally hyperkaehler manifolds, describing them in terms of 3-Sasakian geometry. Similar results are proven for compact Einstein-Weyl locally conformal Kaehler manifolds.

Affiliated with

Also associated with

No associations

Rating

Vanishing theorems for locally conformal hyperkaehler 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 Vanishing theorems for locally conformal hyperkaehler manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vanishing theorems for locally conformal hyperkaehler manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-721773