Simply connected spin manifolds with positive scalar curvature
نویسندگان
چکیده
منابع مشابه
Simply Connected Manifolds of Positive Scalar Curvature
Hitchin proved that if M is a spin manifold with positive scalar curvature, then the A^O-characteristic number a(M) vanishes. Gromov and Lawson conjectured that for a simply connected spin manifold M of dimension > 5, the vanishing of a(M) is sufficient for the existence of a Riemannian metric on M with positive scalar curvature. We prove this conjecture using techniques from stable homotopy th...
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For each n 2 3, we present a family of Riemannian metrics g on W” such that each Riemannian manifold M” = (IT’, g) has positive bottom of the spectrum of Laplacian A, (M”) > 0 and bounded geometry 1 K 1 < C but M” admits no non-constant bounded harmonic functions. These Riemannian manifolds mentioned above give a negative answer to a problem addressed by Schoen-Yau [ 181 in dimension n > 3.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1985
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1985-0776211-4