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Curvature and stability of vector bundles. (English) Zbl 0546.53041
The author announces differential geometric conditions for a holomorphic vector bundle to be stable or semi-stable. The Einstein condition is discussed in this context [see Nagoya Math. J. 77, 5-11, (1980; Zbl 0432.53049)] and several examples for hermitian vector bundles satisfying this condition are presented.
Reviewer: Bernd Wegner

##### MSC:
 53C55 Global differential geometry of Hermitian and Kählerian manifolds
##### Keywords:
holomorphic vector bundle; stable; Einstein condition
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##### References:
 [1] M. Itoh: Moduli of anti-self-dual connections on Kahler manifolds. Proc. Japan Acad., 57A, 176-180 (1981). · Zbl 0493.58018 · doi:10.3792/pjaa.57.176 [2] S. Kobayashi: First Chern class and holomorphic tensor fields. Nagoya Math. J., 77, 5-11 (1980). · Zbl 0432.53049 [3] M. Lubke: Chern classes of Hermitian-Einstein vector bundles (to appear). [4] F. Takemoto: Stable vector bundles on algebraic surfaces. Nagoya Math. J., 47, 29-48 (1972). · Zbl 0245.14007 [5] H. Umemura: Stable vector bundles with numerically trivial Chern classes over a hyperelliptic surface, ibid., 59, 107-134 (1975). · Zbl 0337.14025 [6] H. Umemura: On a theorem of Ramanan. ibid., 69, 131-138 (1978). · Zbl 0345.14017
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