Eigenvalue estimates for 3-Sasaki structures

Abstract We obtain new lower bounds for the first non-zero eigenvalue of scalar sub-Laplacian 3-Sasaki metrics, improving Lichnerowicz–Obata-type estimates by Ivanov, Petkov and Vassilev (2013, 2014). The limiting eigenspace is fully described in terms automorphism algebra. Our results can be thought as an analogue Lichnerowicz–Matsushima estimate Kähler–Einstein metrics. In dimension 7, if algebra non-vanishing, we also compute second construct explicit eigenfunctions. addition, all metrics canonical variation metric give a bound spectrum Riemannian Laplace operator, depending only on curvature dimension. strengthen result pertaining to growth rate harmonic functions, due Conlon, Hein Sun 2017), case hyperkähler cones. this setup describe space holomorphic functions.