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A characterization of the ball by its intrinsic metrics. (English) Zbl 0501.32002

MSC:
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32F45 Invariant metrics and pseudodistances in several complex variables
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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References:
[1] Gray, A., Vanhecke, L.: Almost hermitian manifolds with constant holomorphic sectional curvature. ?asopis P?st. Mat.104, 170-179 (1979) · Zbl 0413.53011
[2] Hörmander, L.: An introduction to complex analysis in several variables. Princeton: Van Nostrand 1966 · Zbl 0138.06203
[3] Kobayashi, S.: Hyperbolic manifolds and holomorphic mappings. New York: Dekker 1970 · Zbl 0207.37902
[4] Kobayashi, S.: Intrinsic distances, measures, and geometric function theory. Bull. AMS82, 357-416 (1976) · Zbl 0346.32031 · doi:10.1090/S0002-9904-1976-14018-9
[5] Rosay, J.-P.: Sur une caractérisation de la boule parmi les domaines de ? n par son groupe d’automorphismes. Ann. l’Inst. Fourier29, 91-97 (1979) · Zbl 0402.32001
[6] Royden, H.L.: Remarks on the Kobayashi metric. In: Several complex variables. II. Lecture Notes in Mathematics, Vol. 185, pp. 125-137. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0218.32012
[7] Rudin, W.: Function theory in the unit ball of ? n . Berlin, Heidelberg, New York: Springer 1980 · Zbl 0495.32001
[8] Stanton, C.M.: A characterization of the polydisc. Math. Ann.253, 129-135 (1980) · Zbl 0453.32008 · doi:10.1007/BF01578908
[9] Wong, B.: Characterization of the unit ball in ? n by its automorphism group. Invent. Math.41, 253-257 (1977) · Zbl 0385.32016 · doi:10.1007/BF01403050
[10] Wong, B.: On the holomorphic curvature of some intrinsic metrics. Proc. AMS65, 57-61 (1977) · Zbl 0364.32009 · doi:10.1090/S0002-9939-1977-0454081-7
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