Dirac eigenvalues and total scalar curvature
نویسندگان
چکیده
منابع مشابه
σk-SCALAR CURVATURE AND EIGENVALUES OF THE DIRAC OPERATOR
On a 4-dimensional closed spin manifold (M, g), the eigenvalues of the Dirac operator can be estimated from below by the total σ2-scalar curvature of M 4 as follows λ 4 ≥ 32 3 R M4 σ2(g)dvol(g) vol(M, g) . Equality implies that (M, g) is a round sphere and the corresponding eigenspinors are Killing spinors. Dedicated to Professor Wang Guangyin on the occasion of his 80th birthday
متن کاملDirac eigenvalues and total scalar curvature Bernd Ammann and Christian Bär
It has recently been conjectured that the eigenvalues λ of the Dirac operator on a closed Riemannian spin manifold M of dimension n ≥ 3 can be estimated from below by the total scalar curvature: λ 2 ≥ n 4(n − 1) · ∫ M S vol(M) . We show by example that such an estimate is impossible. 1991 Mathematics Subject Classification: 58G25
متن کاملm at h . D G / 9 90 90 61 11 S ep 1 99 9 Dirac eigenvalues and total scalar curvature
It has recently been conjectured that the eigenvalues λ of the Dirac operator on a closed Riemannian spin manifold M of dimension n ≥ 3 can be estimated from below by the total scalar curvature: λ ≥ n 4(n− 1) · ∫ M S vol(M) . We show by example that such an estimate is impossible. 1991 Mathematics Subject Classification: 58G25
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We give a sharp extrinsic lower bound for the first eigenvalues of the intrinsic Dirac operator of certain hypersurfaces bounding a compact domain in a spin manifold of negative scalar curvature. Limiting-cases are characterized by the existence, on the domain, of imaginary Killing spinors. Some geometrical applications, as an Alexandrov type theorem, are given. Mathematics Subject Classificati...
متن کاملThe First Dirac Eigenvalue on Manifolds with Positive Scalar Curvature
We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich’s eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2000
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(99)00050-9