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EIGENVALUES ESTIMATES FOR THE DIRAC OPERATOR IN TERMS OF CODAZZI TENSORS
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 Title & Authors
EIGENVALUES ESTIMATES FOR THE DIRAC OPERATOR IN TERMS OF CODAZZI TENSORS
Friedrich, Thomas; Kim, Eui-Chul;
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 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 crossref(new window)
2.
SASAKIAN TWISTOR SPINORS AND THE FIRST DIRAC EIGENVALUE,;

대한수학회지, 2016. vol.53. 6, pp.1347-1370 crossref(new window)
1.
Estimates of small Dirac eigenvalues on 3-dimensional Sasakian manifolds, Differential Geometry and its Applications, 2010, 28, 6, 648  crossref(new windwow)
2.
DIRAC EIGENVALUES ESTIMATES IN TERMS OF DIVERGENCEFREE SYMMETRIC TENSORS, Bulletin of the Korean Mathematical Society, 2009, 46, 5, 949  crossref(new windwow)
3.
SASAKIAN TWISTOR SPINORS AND THE FIRST DIRAC EIGENVALUE, Journal of the Korean Mathematical Society, 2016, 53, 6, 1347  crossref(new windwow)
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2.
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3.
Th. Friedrich, Dirac Operators in Riemannian Geometry, Graduate Studies in Mathematics, 25. American Mathematical Society, Providence, RI, 2000

4.
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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 crossref(new window)

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

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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 crossref(new window)

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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 crossref(new window)