Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds
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Publication:6326515
DOI10.1007/S00229-021-01358-8arXiv1910.01621MaRDI QIDQ6326515
Publication date: 3 October 2019
Abstract: Sasakian manifolds are odd-dimensional counterpart to Kahler manifolds. They can be defined as contact manifolds equipped with an invariant Kahler 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 on Vaisman and Sasakian manifolds. We construct a Lie superalgebra associated to a Sasakian manifold in the same way as the Kahler supersymmetry algebra is associated to a Kahler manifold. We use this construction to produce a self-contained, coordinate-free proof of the results by Tachibana, Kashiwada and Sato on the decomposition of harmonic forms and cohomology of Sasakian and Vaisman manifolds. In the last section, we compute the supersymmetry algebra of Sasakian manifolds explicitly.
Global differential geometry of Hermitian and Kählerian manifolds (53C55) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) de Rham theory in global analysis (58A12) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)
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