Abstract:We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provide a new type of EinsteinDirac coupling. We establish a special method for constructing global smooth solutions of a newly derived Einstein-Dirac system called the CL-Einstein-Dirac equation of type II (see Definition 3.1).
Abstract. Let (M 3 , g) be a 3-dimensional closed Sasakian spin manifold. Let S min denote the minimum of the scalar curvature of (M 3 , g). Let λ . In this paper, we remove the restriction "if λ for S min ≥ 30.
Abstract. On a closed eta-Einstein Sasakian spin manifold of dimension 2m + 1 ≥ 5, m ≡ 0 mod 2, we prove a new eigenvalue estimate for the Dirac operator. In dimension 5, the estimate is valid without the eta-Einstein condition. Moreover, we show that the limiting case of the estimate is attained if and only if there exists such a pair (ϕ m 2 −1 , ϕ m 2 ) of spinor fields (called Sasakian duo, see Definition 2.1) that solves a special system of two differential equations.
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