2023/12/12 by Li, Ping, Sun, Xiaomei, Zhu, Anqiang
#53C55 #58C40 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2312.07259
We are concerned in this article with a classical topic in spectral geometry dating back to McKean-Singer, Patodi and Tanno: whether or not the constancy of sectional curvature (resp. holomorphic sectional curvature) of a compact Riemannian manifold (resp. Kähler manifold) can be completely determined by the eigenvalues of its p-Laplacian for a single integer p? We treat this question under two conditions: gradient shrinking Ricci soliton for Riemannian manifolds and cohomologically Einstein for Kähler manifolds. We show that, with some sporadic unknown cases, this is true for each p. Furthermore, we show that the condition of being isospectral can be relaxed to a suitable almost-isospectral version.