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Compact Hermitian surfaces of constant antiholomorphic sectional curvatures |
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| Authors: | Vestislav Apostolov Georgi Ganchev Stefan Ivanov |
| Institution: | Bulgarian Academy of Science, Institute of Mathematics Acad., G. Bonchev Str., blok 8, 1113 Sofia Bulgaria Georgi Ganchev ; Bulgarian Academy of Science, Institute of Mathematics Acad., G. Bonchev Str., blok 8, 1113 Sofia Bulgaria ; University of Sofia, Faculty of Mathematics and Informatics, Department of Geometry, bul. James Bouchier 5, 1164 Sofia, Bulgaria |
| 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. |
| Keywords: | Compact Hermitian surfaces antiholomorphic Riemannian and antiholomorphic Hermitian sectional curvatures self-dual Hermitian surfaces |
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