Betti numbers of nearly G₂ and nearly Kähler manifolds with Weyl curvature bounds

2023/03/31 by Iliashenko, Anton
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.18208

Abstract

In this paper we use the Weitzenböck formulas to get information about the Betti numbers of compact nearly G₂ and compact nearly Kähler 6-manifolds. First, we establish estimates on two curvature-type self adjoint operators on particular spaces assuming bounds on the sectional curvature. Then using the Weitzenböck formulas on harmonic forms, we get results of the form: if certain lower bounds hold for these curvature operators then certain Betti numbers are zero. Finally, we combine both steps above to get sufficient conditions of vanishing of certain Betti numbers based on the bounds on the sectional curvature.

Related

• Integral Curvature Bounds and Betti Numbers
• Decomposition of the Curvature Operator and Applications to the Hopf Conjecture
• Topological bounds on hyperkähler manifolds
• Hodge theoretic results for nearly Kähler manifolds in all dimensions
• Boundness of b₂ for hyperkähler manifolds with vanishing odd-Betti numbers