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Proceedings of the American Mathematical Society

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Lefschetz decompositions for eigenforms on a Kähler manifold


Author: Donu Arapura
Journal: Proc. Amer. Math. Soc. 146 (2018), 2277-2281
MSC (2010): Primary 58J50; Secondary 14C30
DOI: https://doi.org/10.1090/proc/14006
Published electronically: February 8, 2018
MathSciNet review: 3767377
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Abstract: We show that the eigenspaces of the Laplacian $\Delta _k$ on $k$-forms on a compact Kähler 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 $\Delta _{k+1}$ for $k<\dim X$.


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Additional Information

Donu Arapura
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
MR Author ID: 26770

Received by editor(s): August 9, 2017
Published electronically: February 8, 2018
Additional Notes: This research was partially supported by the NSF
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society