Some Q-curvature Operators on Five-Dimensional Pseudohermitian Manifolds

We construct Q-curvature operators on d-closed (1, 1)-forms and on ∂¯ b-closed (0, 1)-forms on five-dimensional pseudohermitian manifolds. These closely related operators give rise to a new formula for the scalar Q-curvature. As applications, we give a cohomological characterization of CR five-manifolds which admit a Q-flat contact form, and we show that every closed, strictly pseudoconvex CR five-manifold with trivial first real Chern class admits a Q-flat contact form provided the Q-curvature operator on ∂¯ b-closed (0, 1)-forms is nonnegative.

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s12220-022-01170-0

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Work Title Some Q-curvature Operators on Five-Dimensional Pseudohermitian Manifolds
Access
Open Access
Creators
  1. Jeffrey S. Case
Keyword
  1. Q-curvature
  2. Q-flat contact form
  3. Invariant differential operators
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Journal of Geometric Analysis
Publication Date February 24, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/s12220-022-01170-0
Deposited January 23, 2024

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    Keyword
    • Q-curvature, Q-flat contact form, Invariant differential operators
  • Updated