Th. Friedrich and E.C. Kim, The Einstein-Dirac equation on Riemannian spin manifolds, Journ. Geom. Phys. 33 (2000), 128-172. Home/Search Document Details and Download
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Eigenvalue Estimates For The Dirac Operator On Warped.. - Kraus, Tretter (2000) (Correct)
....of B 0 f S k and therefore with the spin structures on B 0 . The spinor calculus for warped products with 1 dimensional basis has been discussed in [6, p. 18] and [5] the formulas for the Cli ord multiplication on products have been established in [8] and more explicitly by Kramer [13] In [11] the spinor calculus on products has been worked out in some special dimensions. In the sequel we summarize these and present the spinor calculus on warped products M 0 = B 0 f S k over an m dimensional basis B. We use the following notations: Notation. For a Riemannian spin manifold X we ....
Th. Friedrich, E.C. Kim, The Einstein Dirac equation on Riemannian spin manifolds, J. Geom. Phys. 33 (2000), 128-172.
Killing Spinors in Supergravity with 4-Fluxes - Agricola, Friedrich Self-citation (Friedrich) (Correct)
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Th. Friedrich and E.C. Kim, The Einstein-Dirac equation on Riemannian spin manifolds, Journ. Geom. Phys. 33 (2000), 128-172.
Parallel Spinors and Connections with Skew-Symmetric Torsion .. - Friedrich, Ivanov (2001) (4 citations) Self-citation (Friedrich) (Correct)
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Th. Friedrich, E. C. Kim, The Einstein-Dirac equation on Riemannian spin manifolds, Journ. Geom. Phys. 33 (2000), 128-172.
The Casimir Operator of a Metric Connection with.. - Agricola, Friedrich Self-citation (Friedrich) (Correct)
....second case for spinors in the kernel is given by D = 0 and T = 4 . The spinor eld is an eigenspinor for the Riemannian Dirac operator, D = The formulas of Proposition 3.2 and Proposition 3. 5 yield in the compact case two conditions: 12 0 and 5 Scal 16: The paper [15] contains a construction of Sasakian manifolds admitting a spinor eld of that algebraic type in the kernel of D . We describe the construction explicitely. Suppose that the Riemannian Ricci tensor of a simply connected, 5 dimensional Sasakian manifold is given by the formula = 2 g 6 ....
....of a simply connected, 5 dimensional Sasakian manifold is given by the formula = 2 g 6 : Its scalar curvature equals Scal = 4. In the simply connected and compact case, they are total spaces of S principal bundles over 4 dimensional Calabi Yau orbifolds (see [5] There exist (see [15], Theorem 6.3) two spinor elds 1 , 2 such that 1 X 1 3 (X) 1 ; T 1 = 4 1 ; 1 X 2 (X) 2 ; T 2 = 4 2 : 1 = 1 ; T 1 = 4 1 ; and D 2 = 2 ; T 2 = 4 2 ; and therefore the spinor elds 1 and 2 belong to the kernel of the operator D . ....
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Th. Friedrich and E.C. Kim, The Einstein-Dirac equation on Riemannian spin manifolds, Journ. Geom. Phys. 33 (2000), 128-172.
Parallel Spinors and Connections with Skew-Symmetric Torsion .. - Friedrich, Ivanov (2001) (4 citations) Self-citation (Friedrich) (Correct)
....Indeed, consider a simply connected Kahler Einstein manifold (N 4 ; J; g ) with scalar curvature Scal = 32. Then there exists an S 1 bundle M 5 N 4 as well as a Sasakian structure on M 5 such that the Ricci tensor has the eigenvalues Ric g = diag(6; 6; 6; 6; 4) see [19]) More general, the Tanno deformation of an arbitrary 5 dimensional Einstein Sasakian structure yields for a special value of deformation parameter examples of Sasakian manifolds satisfying the condition of Theorem 7.3 (see Example 9.3) The Einstein Sasakian manifolds constructed recently in [6] ....
....torsion (Theorem 8.2) 26 Since r = 0 the (restricted) holonomy group Hol r of r is contained in U(k) This group cannot occur as the isotropy group of any spinor. The spinor bundle Sigma of a contact spin manifold decomposes under the action of the fundamental form F into the sum (see [19]) Sigma = Sigma 0 Phi : Sigma k ; dim( Sigma r ) k r : The isotropy group of a spinor of type Sigma 0 or Sigma k coincides with the subgroup SU(k) ae U(k) Consequently, there exists locally a r parallel spinor of type Sigma 0 ; Sigma k if and only if Hol r is contained ....
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Th. Friedrich, E. C. Kim, The Einstein-Dirac equation on Riemannian spin manifolds, Journ. Geom. Phys. 33 (2000), 128-172.
Solutions of the Einstein-Dirac Equation on Riemannian.. - Friedrich (1 citation) Self-citation (Friedrich) (Correct)
.... is a real constant and T is the energy momentum tensor of the spinor field defined by the formula T (X; Y ) X Delta r Y Y Delta rX ; The scalar curvature S is related to the eigenvalue and the length of the spinor field by the formula S = Sigma n Gamma 2 j j 2 : In [KimF] we introduced the weak Killing equation for a spinor field : rX = n 2(n Gamma 1) dS(X) 2 (n Gamma 2)S Ric(X) Delta Gamma n Gamma 2 X Delta 1 2(n Gamma 1)S X Delta dS Delta Supported by the SFB 288 of the DFG. 1 Any weak Killing spinor ....
....SFB 288 of the DFG. 1 Any weak Killing spinor (WK spinor) yields a solution of the Einstein Dirac equation after normalization = s (n Gamma 2)jSj jjj j 2 : In fact, in dimension n = 3 the Einstein Dirac equation is essentially equivalent to the weak Killing equation (see [KimF]) Up to now the following 3 dimensional Riemannian manifolds admitting WK spinors are known: 1. the flat torus T 3 with a parallel spinor; 2. the sphere S 3 with a Killing spinor; 3. two non Einstein Sasakian metrics on the sphere S 3 admitting WK spinors. The scalar curvature of these two ....
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E.C. Kim and Th. Friedrich, The Einstein-Dirac equation on Riemannian spin manifolds, Journ. Geom. Phys. 33 (2000), 128-172. 12
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