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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compact Hermitian surfaces of constant
antiholomorphic sectional curvatures


Authors: Vestislav Apostolov, Georgi Ganchev and Stefan Ivanov
Journal: Proc. Amer. Math. Soc. 125 (1997), 3705-3714
MSC (1991): Primary 53C15, 53C55, 53B35
MathSciNet review: 1415572
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Abstract: Compact Hermitian surfaces of constant antiholomorphic sectional curvatures with respect to the Riemannian curvature tensor and with respect to the Hermitian curvature tensor are considered. It is proved: a compact Hermitian surface of constant antiholomorphic Riemannian sectional curvatures is a self-dual Kaehler surface; a compact Hermitian surface of constant antiholomorphic Hermitian sectional curvatures is either a Kaehler surface of constant (non-zero) holomorphic sectional curvatures or a conformally flat Hermitian surface.


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Additional Information

Georgi Ganchev
Affiliation: Bulgarian Academy of Science, Institute of Mathematics Acad., G. Bonchev Str., blok 8, 1113 Sofia Bulgaria
Email: ganchev@math.acad.bg

Stefan Ivanov
Affiliation: University of Sofia, Faculty of Mathematics and Informatics, Department of Geometry, bul. James Bouchier 5, 1164 Sofia, Bulgaria
Email: ivanovsp@fmi.uni-sofia.bg

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04043-4
PII: S 0002-9939(97)04043-4
Keywords: Compact Hermitian surfaces, antiholomorphic Riemannian and antiholomorphic Hermitian sectional curvatures, self-dual Hermitian surfaces
Received by editor(s): March 22, 1995
Received by editor(s) in revised form: July 28, 1996
Additional Notes: The first author was supported by Contract MM 423/1994 with the Ministry of Science and Education of Bulgaria; the second author was supported by Contract MM 413/1994 with the Ministry of Science and Education of Bulgaria; and the third author was supported by Contract MM 413/1994 with the Ministry of Science and Education of Bulgaria and by Contract 219/1994 with the University of Sofia “St. Kl. Ohridski"
Communicated by: Christopher Croke
Article copyright: © Copyright 1997 American Mathematical Society