Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On almost Einstein holomorphic vector bundles over Hermitian surfaces
HTML articles powered by AMS MathViewer

by Novica Blažić PDF
Proc. Amer. Math. Soc. 110 (1990), 201-209 Request permission

Abstract:

We study holomorphic vector bundles $\left ( {E,h} \right )$ of rank 2 over a compact Hermitian surface $\left ( {M,g} \right )$. Then the notion of a metric with a $k$-pinched Ricci curvature is introduced and it represents the generalization of the Einstein condition. Some necessary topological conditions for existence of a metric $h$ with $k$-pinched $\left ( {0 \leq k \leq 1} \right )$ Ricci curvature are obtained.
References
  • M. Berger, Sur les variétés d’Einstein compactes, Comptes Rendus de la IIIe Réunion du Groupement des Mathématiciens d’Expression Latine (Namur, 1965) Librairie Universitaire, Louvain, 1966, pp. 35–55 (French). MR 0238226
  • Lionel Bérard-Bergery, Marcel Berger, and Christian Houzel (eds.), Géométrie riemannienne en dimension 4, Textes Mathématiques [Mathematical Texts], vol. 3, CEDIC, Paris, 1981 (French). Papers from the Arthur Besse seminar held at the Université de Paris VII, Paris, 1978/1979. MR 769127
  • Novica Blažić, Chern classes of complex vector bundles over almost complex manifolds, Boll. Un. Mat. Ital. B (7) 3 (1989), no. 4, 939–951 (English, with Italian summary). MR 1032619, DOI 10.1016/0012-365x(72)90120-3
  • Bang-yen Chen and Koichi Ogiue, Some characterizations of complex space forms in terms of Chern classes, Quart. J. Math. Oxford Ser. (2) 26 (1975), no. 104, 459–464. MR 405303, DOI 10.1093/qmath/26.1.459
  • Paul Gauduchon, La topologie d’une surface hermitienne d’Einstein, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 11, A509–A512 (French, with English summary). MR 571563
  • Peter B. Gilkey, The index theorem and the heat equation, Mathematics Lecture Series, No. 4, Publish or Perish, Inc., Boston, Mass., 1974. Notes by Jon Sacks. MR 0458504
  • A. Gray, M. Barros, A. M. Naveira, and L. Vanhecke, The Chern numbers of holomorphic vector bundles and formally holomorphic connections of complex vector bundles over almost complex manifolds, J. Reine Angew. Math. 314 (1980), 84–98. MR 555906
  • Shoshichi Kobayashi, Differential geometry of complex vector bundles, Publications of the Mathematical Society of Japan, vol. 15, Princeton University Press, Princeton, NJ; Princeton University Press, Princeton, NJ, 1987. Kanô Memorial Lectures, 5. MR 909698, DOI 10.1515/9781400858682
  • Shoshichi Kobayashi, Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 4, 158–162. MR 664562
  • Martin Lübke, Chernklassen von Hermite-Einstein-Vektorbündeln, Math. Ann. 260 (1982), no. 1, 133–141 (German). MR 664372, DOI 10.1007/BF01475761
  • Albert Polombo, Nombres caractéristiques d’une variété riemannienne de dimension $4$, J. Differential Geometry 13 (1978), no. 1, 145–162 (French). MR 520607
Similar Articles
Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 110 (1990), 201-209
  • MSC: Primary 53C25; Secondary 32L05, 53C55, 57R20
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1023350-0
  • MathSciNet review: 1023350