Revisiting 3-Sasakian and $G_2$-structures

TY - UNPB

T1 - Revisiting 3-Sasakian and $G_2$-structures

AU - Salamon, Simon

AU - Singhal, Ragini

N1 - 21 pages

PY - 2024/12/27

Y1 - 2024/12/27

N2 - The algebra of exterior differential forms on a regular 3-Sasakian 7-manifold is investigated, with special reference to nearly-parallel G_2 3-forms. This is applied to the study of 3-forms invariant under cohomogeneity-one actions by SO(4) on the 7-sphere and on Berger's space SO(5)/SO(3).

AB - The algebra of exterior differential forms on a regular 3-Sasakian 7-manifold is investigated, with special reference to nearly-parallel G_2 3-forms. This is applied to the study of 3-forms invariant under cohomogeneity-one actions by SO(4) on the 7-sphere and on Berger's space SO(5)/SO(3).

KW - math.DG

KW - hep-th

KW - 53C25 (Primary) 53C29, 53C30 (Secondary)

M3 - Preprint

BT - Revisiting 3-Sasakian and $G_2$-structures

ER -