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-...

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Bibliographic Details
Published in:	The Journal of geometric analysis Vol. 33; no. 4
Main Author:	Case, Jeffrey S.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-04-2023 Springer Nature B.V
Subjects:	Abstract Harmonic Analysis Convex and Discrete Geometry Curvature Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Operators (mathematics) Secondary 58A10 Invariant differential operators Primary 32V05 flat contact form 58J10 curvature
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Summary:	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.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-022-01170-0