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On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1 \geq 5, \, m \, \equiv 0 \, \mbox{mod} \, 2,$ 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 $(\varphi_{\frac{m}{2} -1} , \, \varphi_{\frac{m}{2}} )$ of spinor fields (called {\it Sasakian duo}, see Definition 2.1) that solves a special system of two differential equations.
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참고문헌 (21)
참고문헌 신청
I. Agricola / 2006 / The Srni lectures on non-integrable geometries with torsion / Arch. Math. (Brno) 42:5~84
I. Agricola / 2013 / Twistorial eigenvalue estimates for generalized Dirac operators with torsion / Adv. Math 243:296~329
I. Agricola / 2008 / Th. Friedrich, and M. Kassuba, Eigenvalue estimates for Dirac operators with parallel characteristic torsion / Differential Geom. Appl 26(6):613~624
C. B¨ar / 1993 / Real Killing spinors and holonomy / Comm. Math. Phys 154(3):509~521
H. Baum / 1991 / Twistors and Killing Spinors on Riemannian Manifolds / Teubner
I. Agricola / 2013 / Twistorial eigenvalue estimates for generalized Dirac operators with torsion / Adv. Math 243:296~329
I. Agricola / 2008 / Th. Friedrich, and M. Kassuba, Eigenvalue estimates for Dirac operators with parallel characteristic torsion / Differential Geom. Appl 26(6):613~624
C. B¨ar / 1993 / Real Killing spinors and holonomy / Comm. Math. Phys 154(3):509~521
H. Baum / 1991 / Twistors and Killing Spinors on Riemannian Manifolds / Teubner
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