scholarly journals Lower bounds for the eigenvalue estimates of the submanifold Dirac operator

2021 ◽  
Author(s):  
Yongfa Chen
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Eigenvalue Estimates

scholarly journals ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

2002 ◽  
Vol 13 (05) ◽  
pp. 533-548 ◽  
Author(s):  
NICOLAS GINOUX ◽  
BERTRAND MOREL
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Dirac Operators ◽  
Extrinsic Curvature ◽  
Eigenvalue Estimates ◽  
Killing Spinors ◽  
Spinor Fields ◽  
Twisted Dirac Operators

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

scholarly journals Eigenvalue estimates of the Dirac operator depending on the Ricci tensor

2002 ◽  
Vol 324 (4) ◽  
pp. 799-816 ◽  
Author(s):  
T. Friedrich ◽  
K.-D. Kirchberg
Keyword(s):  
Dirac Operator ◽  
Ricci Tensor ◽  
Eigenvalue Estimates

scholarly journals Eigenvalue estimates for the Dirac operator depending on the Weyl tensor

2002 ◽  
Vol 41 (3) ◽  
pp. 196-207 ◽  
Author(s):  
Thomas Friedrich ◽  
Klaus-Dieter Kirchberg
Keyword(s):  
Dirac Operator ◽  
Weyl Tensor ◽  
Eigenvalue Estimates

Vanishing Theorems and Eigenvalue Estimates in Riemannian Spin Geometry

1997 ◽  
Vol 08 (07) ◽  
pp. 921-934 ◽  
Author(s):  
Thomas Branson ◽  
Oussama Hijazi
Keyword(s):  
Representation Theory ◽  
Dirac Operator ◽  
Differential Operators ◽  
Structure Group ◽  
Vanishing Theorems ◽  
Eigenvalue Estimates ◽  
Spin Geometry ◽  
First Order ◽  
Group Spin

We use the representation theory of the structure group Spin (n), together with the theory of conformally covariant differential operators, to generalize results estimating eigenvalues of the Dirac operator to other tensor-spinor bundles, and to get vanishing theorems for the kernels of first-order differential operators.

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