EIGENVALUES ESTIMATES FOR THE DIRAC OPERATOR IN TERMS OF CODAZZI TENSORS

Title & Authors
EIGENVALUES ESTIMATES FOR THE DIRAC OPERATOR IN TERMS OF CODAZZI TENSORS
Friedrich, Thomas; Kim, Eui-Chul;

Abstract
We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2]
Keywords
Dirac operator;eigenvalues;Codazzi tensors;
Language
English
Cited by
1.
DIRAC EIGENVALUES ESTIMATES IN TERMS OF DIVERGENCEFREE SYMMETRIC TENSORS,;

대한수학회보, 2009. vol.46. 5, pp.949-966
1.
Estimates of small Dirac eigenvalues on 3-dimensional Sasakian manifolds, Differential Geometry and its Applications, 2010, 28, 6, 648
2.
DIRAC EIGENVALUES ESTIMATES IN TERMS OF DIVERGENCEFREE SYMMETRIC TENSORS, Bulletin of the Korean Mathematical Society, 2009, 46, 5, 949
3.
SASAKIAN TWISTOR SPINORS AND THE FIRST DIRAC EIGENVALUE, Journal of the Korean Mathematical Society, 2016, 53, 6, 1347
References
1.
A. Besse, Einstein Manifolds, Springer-Verlag, Berlin, 1987

2.
Th. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten, Riemann-schen Mannigfaltigkeit nichtnegativer Skalarkrummung, Math. Nachr. 97 (1980), 117-146

3.
Th. Friedrich, Dirac Operators in Riemannian Geometry, Graduate Studies in Mathematics, 25. American Mathematical Society, Providence, RI, 2000

4.
Th. Friedrich and E. C. Kim, Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors, J. Geom. Phys. 37 (2001), no. 1-2, 1-14

5.
Th. Friedrich and K.-D. Kirchberg, Eigenvalue estimates of the Dirac operator depending on the Ricci tensor, Math. Ann. 324 (2002), no. 4, 799-816

6.
E. C. Kim, A local existence theorem for the Einstein-Dirac equation, J. Geom. Phys. 44 (2002), no. 2-3, 376-405

7.
E. C. Kim, The $\hat{A}$-genus and symmetry of the Dirac spectrum on Riemannian product manifolds, Differential Geom. Appl. 25 (2007), no. 3, 309-321

8.
K.-D. Kirchberg, An estimation for the first eigenvalue of the Dirac operator on closed Kahler manifolds of positive scalar curvature, Ann. Global Anal. Geom. 4 (1986), no. 3, 291-325

9.
W. Kramer, U. Semmelmann, and G. Weingart, Eigenvalue estimates for the Dirac operator on quaternionic Kahler manifolds, Math. Z. 230 (1999), no. 4, 727-751