Lefschetz decompositions for eigenforms on a K\"ahler manifold

Donu Arapura

Lefschetz decompositions for eigenforms on a K\"ahler manifold

Differential Geometry 2017-11-01 v2 Algebraic Geometry

Authors: Donu Arapura

Abstract

We show that the eigenspaces of the Laplacian $\Delta_k$ on $k$ -forms on a compact K\"ahler manifold carry Hodge and Lefschetz decompositions. Among other consequences, we show that the positive part of the spectrum of $\Delta_k$ lies in the spectrum of $\Delta_{k+1}$ .

Keywords

kähler manifolds laplacian eigenfunctions

Cite

@article{arxiv.1708.02930,
  title  = {Lefschetz decompositions for eigenforms on a K\"ahler manifold},
  author = {Donu Arapura},
  journal= {arXiv preprint arXiv:1708.02930},
  year   = {2017}
}

Comments

Final revision. To appear in Proc. AMS

Related papers

View all related →