zbMATH — the first resource for mathematics

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
Full Text:
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 [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 [9] Wong, B.: Characterization of the unit ball in ? n by its automorphism group. Invent. Math.41, 253-257 (1977) · Zbl 0385.32016 [10] Wong, B.: On the holomorphic curvature of some intrinsic metrics. Proc. AMS65, 57-61 (1977) · Zbl 0364.32009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.