H-Killing Spinors and Spinorial Duality for Homogeneous 3-(α,δ)-Sasaki Manifolds

2023/09/28 by Agricola, Ilka, Hofmann, Jordan
#53C25 #53C27 #53C30 #53D10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.16610

Abstract

We show that 3-(α,δ)-Sasaki manifolds admit solutions of a certain new spinorial field equation (the H-Killing equation) generalizing the well-known Killing spinors on 3-Sasakian manifolds. These H-Killing spinors have more desirable geometric properties than the spinors obtained by simply deforming a 3-Sasakian metric; in particular we obtain a one-to-one correspondence between H-Killing spinors on dual pairs of homogeneous 3-(α,δ)-Sasaki spaces. Finally, we show that H-Killing spinors generalize certain special spinors in dimension 7 previously constructed by Agricola-Friedrich and Agricola-Dileo using G₂-geometry.

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