The first positive eigenvalue of the Dirac operator on 3-dimensional Sasakian manifolds
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
Abstract. Let (M3, g) be a 3-dimensional closed Sasakian spin manifold. Let Smin denote the minimum of the scalar curvature of (M3, g). Let λ+ 1 > 0 be the first positive eigenvalue of the Dirac operator of (M3, g). We proved in [13] that if λ+ 1 belongs to the interval λ+∈(1/2 , 5/2) , then λ+ 1 satisfies λ+ 1 ≥ Smin+6/8 . In this paper, we remove the restriction “if λ+ 1 belongs to the interval λ+ 1 ∈ ( 1/2 , 5/2)” and prove [수식]
Abstract
Abstract. Let (M3, g) be a 3-dimensional closed Sasakian spin manifold. Let Smin denote the minimum of the scalar curvature of (M3, g). Let λ+ 1 > 0 be the first positive eigenvalue of the Dirac operator of (M3, g). We proved in [13] that if λ+ 1 belongs to the interval λ+∈(1/2 , 5/2) , then λ+ 1 satisfies λ+ 1 ≥ Smin+6/8 . In this paper, we remove the restriction “if λ+ 1 belongs to the interval λ+ 1 ∈ ( 1/2 , 5/2)” and prove [수식]
참고문헌 (15)
- I. Agricola, "The Srn´ı lectures on non-integrable geometries with torsion", Arch. Math, 42, pp.5~84 (2006)
- M. F. Atiyah, "Spectral asymmetry and Riemannian geometry", Proc. Cambridge Philos. Soc, 77, pp.43~69 (1975)
- F. A. Belgun, "Normal CR structure on compact 3-manifolds", Math. Z, 238(3), pp.441~460 (2001)
- D. E. Blair, "Riemannian Geometry of Contact and Symplectic Manifolds" (2002), Birkhauser
- Th. Friedrich, "Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrummung", Math. Nachr, 97, pp.117~146 (1980)
- Th. Friedrich, "Dirac Operators in Riemannian Geometry, Graduate Studies in Mathematics, vol. 25" (2000), AMS
- Th. Friedrich, "The second Dirac eigenvalue of a nearly parallel G2-manifold", Adv. Appl. Clifford Algebr, 22(2), pp.301~311 (2012)
- Th. Friedrich, "The Einstein-Dirac equation on Riemannian spin manifolds", J. Geom. Phys, 33(1), pp.128~172 (2000)
- N. Ginoux, "The Dirac Spectrum, Lecture Notes in Mathematics" (2009), Springer-Verlag
- O. Hijazi, "Eigenvalues of the Dirac operator on compact Kahler manifolds", Comm. Math. Phys, 160(3), pp.563~579 (1994)
- E. C. Kim, "The A-genus and symmetry of the Dirac spectrum on Riemannian product manifolds", Differential Geom. Appl, 25(3), pp.309~321 (2007)
- 김의철, "Dirac eigenvalues estimates in terms of divergencefree symmetric tensors", 대한수학회보, 46(5), pp.949~966 (2009), 대한수학회
- E. C. Kim, "Estimates of small Dirac eigenvalues on 3-dimensional Sasakian manifolds", Differential Geom. Appl, 28(6), pp.648~655 (2010)
- S. Kobayashi, "Principal fibre bundles with the 1-dimensional toroidal group", Tohoku Math. J, 8, pp.29~45 (1956)
- A. Moroianu, "Operateur de Dirac et submersions riemanniennes", 석사, pp.1996