PreprintCC BY 4.0arXiv
Some vanishing theorems on (p,q) double form and curvature operator of the second kind
Abstract
We establish a Bochner formula for double forms in terms of the curvature operator of the second kind. As an application, we prove that a complete Riemannian manifold of dimension n ≥ 4 with harmonic Weyl tensor and (3(n−1))/4-nonnegative curvature operator of the second kind is either globally conformally equivalent to a space of positive constant curvature or is isometric to a flat manifold. We prove vanishing theorems for the Lichnérowicz Laplacian Δ on (p,q) double forms. These generalize recent results of Nienhaus-Petersen-Wink \cite{NPW23} and Dai-Fu-Lu-Yang \cite{DF24,DFY24,FL1,FLD}.
Related
- Sphere Theorems for 10/3-Positive Curvature Operator of the Second Kind
- New Curvature Operator of the Second Kind Conditions for Rigidity
- Rigidity of Einstein Manifolds under Two Eigenvalue Conditions on the Curvature Operator of the Second Kind
- Vanishing theorems for L2 Dolbeault cohomology groups of projective Hartogs triangles
- Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature
BibTeX
@misc{fu2026some,
title = {{Some vanishing theorems on $(p,q)$ double form and curvature operator of the second kind}},
author = {Hai-Ping Fu and Yao Lu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10325},
eprint = {2610.10325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10325},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Some vanishing theorems on (p,q) double form and curvature operator of the second kind
AU - Hai-Ping Fu
AU - Yao Lu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10325
UR - https://arxiv.org/abs/2610.10325
AB - We establish a Bochner formula for double forms in terms of the curvature operator of the second kind. As an application, we prove that a complete Riemannian manifold of dimension n ≥ 4 with harmonic Weyl tensor and (3(n−1))/4-nonnegative curvature operator of the second kind is either globally conformally equivalent to a space of positive constant curvature or is isometric to a flat manifold. We prove vanishing theorems for the Lichnérowicz Laplacian Δ on (p,q) double forms. These generalize recent results of Nienhaus-Petersen-Wink \cite{NPW23} and Dai-Fu-Lu-Yang \cite{DF24,DFY24,FL1,FLD}.
ER -