A complete Kähler metric of positive curvature on 𝐶ⁿ

A complete Kähler metric of positive curvature on $C^{n}$
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by Paul F. Klembeck PDF

Proc. Amer. Math. Soc. 64 (1977), 313-316 Request permission

A complete Kähler metric of positive curvature on ${{\mathbf {C}}^n}$ is constructed and its importance is discussed.

References

Ch. Blanc and F. Fiala, Le type d’une surface et sa courbure totale, Comment. Math. Helv. 14 (1942), 230–233 (French). MR 6857, DOI 10.1007/BF02565620
Shiing-shen Chern, An elementary proof of the existence of isothermal parameters on a surface, Proc. Amer. Math. Soc. 6 (1955), 771–782. MR 74856, DOI 10.1090/S0002-9939-1955-0074856-1
R. E. Greene and H. Wu, A theorem in complex geometric function theory, Value distribution theory (Proc. Tulane Univ. Program, Tulane Univ., New Orleans, La., 1972-1973) Dekker, New York, 1974, pp. 145–167. MR 0352534
R. E. Greene and H. Wu, Analysis on noncompact Kähler manifolds, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 2, Williams Coll., Williamstown, Mass., 1975) Amer. Math. Soc., Providence, R.I., 1977, pp. 69–100. MR 0460699
Detlef Gromoll and Wolfgang Meyer, On complete open manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75–90. MR 247590, DOI 10.2307/1970682
Shing Tung Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201–228. MR 431040, DOI 10.1002/cpa.3160280203