caa a22 4500 469117478 CHVBK 20180323133128.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF02921384 doi (NATIONALLICENCE)springer-10.1007/BF02921384 Cheung Chi-Keung Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut Chern forms, chern numbers and curvature conditions on a Kähler-Einstein surface [Elektronische Daten] [Chi-Keung Cheung] In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL 2-norm of (3C 2 −C 1 2 )/C 1 2 is sufficiently small, whereC 1 andC 2 are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C 2 −C 1 2 = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature. Mathematica Josephina, Inc., 1992 Chern class nationallicence Chern number nationallicence Kähler-Einstein metric nationallicence negative holomorphic sectional curvature nationallicence The Journal of Geometric Analysis Springer-Verlag 2/2(1992-03-01), 105-119 1050-6926 2:2<105 1992 2 12220 https://doi.org/10.1007/BF02921384 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02921384 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cheung Chi-Keung Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut NATIONALLICENCE 773 0- The Journal of Geometric Analysis Springer-Verlag 2/2(1992-03-01), 105-119 1050-6926 2:2<105 1992 2 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer