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Superpotentials and the cohomogeneity one Einstein equations. (English) Zbl 1097.53028

The authors provide a detailed analysis of the existence of superpotentials in the Ricci-flat case. They successfully use some ideas from convex geometry to prove an interesting classification theorem under suitable hypotheses, for superpotentials of the Hamiltonian form of the cohomogeneity one Ricci-flat equations. Some new examples of superpotentials which do not satisfy the non-null hypothesis are given and their associated first order systems are analyzed. Superpotentials for the case when the cosmological constant is nonzero are briefly discussed as well.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53C80 Applications of global differential geometry to the sciences
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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