Index of Dirac operator and scalar curvature almost non-negative manifolds
نویسندگان
چکیده
منابع مشابه
Dirac Operators on Hypersurfaces of Manifolds with Negative Scalar Curvature
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 کاملσk-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 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.
متن کاملA remark on four-dimensional almost Kähler-Einstein manifolds with negative scalar curvature
Concerning the Goldberg conjecture, we will prove a result obtained by applying the result of Iton in terms of L 2-norm of the scalar curvature.
متن کاملMass and 3-metrics of Non-negative Scalar Curvature
Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over twenty years ago [45, 53], is a remarkable testament to this faith. However, fundamental mathematical questions concerning mass in general relativity remain, a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2003
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2003.v7.n1.a3