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Footnotes and References
Ueber die Transformation der homogenen Differentialausdrücke zweiten Grades, Crelle J. 70 (1869), 46–70. Christoffel’s original symbol {jk i} is now commonly denoted by Γ ijk or {i jk}.
M. Inoue-S. Kobayashi-T. Ochiai, Holomorphic affine connections on compact complex surfaces, J. Fac. Sci. Univ. Tokyo (1980), to appear.
S. Kobayashi-T. Ochiai, Holomorphic projective structures on compact complex surfaces, to appear.
R. Gunning, On Uniformization of Complex Manifolds; The Role of Connections, Math. Notes No. 22, 1978, Princeton Univ. Press.
In this section, the Chern classes ci are considered as elements of H*(M;R) (rather than elements of H*(M;Z)).
pp.73–74 of A. Lascoux-M. Berger, Variétés Kählériennes Compactes, Lecture Notes in Math. No. 154 (1970), Springer-Verlag.
S. T. Yau, Calabi’s conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci. USA 74 (1977), 1798–1799.
K. Kodaira, Pluricanonical systems on algebraic surfaces of general type, J. Math. Soc. Japan 20 (1968), 170–192.
K. Kodaira, On compact complex analytic surfaces II, Ann. Math. 77 (1963), 563–626; III 78 (1963), 1–40.
K. Maehara, On elliptic surfaces whose first Betti numbers are odd, Intl. Symp. Alg. Geometry, Kyoto, 1977, 565–574.
For Hopf surfaces, see K. Kodaira, On the structure of compact complex analytic surfaces II, Amer. J. Math. 88 (1966), 682–721.
See Note 7).
M. Inoue, On surfaces of class VII0, Inventiones Math. 24 (1974), 269–310.
F. A. Bogomolov, Classification of surfaces of class VII0 with b2=0, Math. USSR Izvestija 10 (1976), 255–269. See also the review of this paper by M. Reid in Math. Reviews, vol. 55, #359.
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Kobayashi, S. (1981). On holomorphic connections. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088853
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DOI: https://doi.org/10.1007/BFb0088853
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