Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds

Sasakian manifolds are odd-dimensional counterpart to Kähler manifolds. They can be defined as contact equipped with an invariant structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition Vaisman construct Lie superalgebra associated in same way supersymmetry algebra manifold. use construction produce self-contained, coordinate-free proof results Tachibana, Kashiwada Sato cohomology In last section, we compute explicitly.