caa a22 4500 475738713 CHVBK 20180406123453.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1007/PL00005792 doi (NATIONALLICENCE)springer-10.1007/PL00005792 Yang DaGang Mathematics Department, Tulane University, New Orleans, LA 70118, USA (e-mail: dgy@math.tulane.edu), US aut Rigidity of Einstein 4-manifolds with positive curvature [Elektronische Daten] [DaGang Yang] Abstract. : An Einstein metric with positive scalar curvature on a 4-manifold is said to be normalized if Ric=1. A basic problem in Riemannian geometry is to classify Einstein 4-manifolds with positive sectional curvature in the category of either topology, diffeomorphism, or isometry. It is shown in this paper that if the sectional curvature K of a normalized Einstein 4-manifold M satisfies the lower bound K≥ε0, ε0≡( -23)/120≈0.102843, or condition (b) of Theorem 1.1, then it is isometric to either S 4, RP 4 with constant sectional curvature K=1/3, or CP 2 with the normalized Fubini-Study metric. As a consequence, both the normalized moduli spaces of Einstein metrics which satisfy either one of the above two conditions on S 4 and CP 2 contain only a single point. In particular, if M is a smooth 4-manifold which is homeomorphic to either S 4, RP 4, or CP 2 but not diffeomorphic to any of the three manifolds, then it can not support any normalized Einstein metric which satisfies either one of the conditions. Springer-Verlag Berlin Heidelberg, 2000 https://doi.org/10.1007/PL00005792 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00005792 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yang DaGang Mathematics Department, Tulane University, New Orleans, LA 70118, USA (e-mail: dgy@math.tulane.edu), US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer