Year: 2026
Type: preprint
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 $n \ge 4$ with harmonic Weyl tensor and $\frac{3(n-1)}{4}$-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}.
Source: arXiv (Cornell University)
Authors: Fu, Hai-Ping, Lu, Yao
Institution: Nanchang University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2772045997, G8317361627, G8733299378
OpenAlex ID: W7220901231