Asymptotic rigidity of Hadamard 2-spaces. (English) Zbl 0984.53014

Nagano, Koichi

J. Math. Soc. Japan 52, No. 4, 699-723 (2000).

Locally compact, geodesically complete 2-dimensional Hadamard spaces whose Tits ideal boundaries have the minimal diameter equal to \( \pi \), are classified. Moreover, the author gives a classification of the universal covering spaces of certain 2-dimensional nonpositively curved spaces. This is an extension of the result obtained in the polyhedral case by W. Ballmann and M. Brin [Publ. Math., Inst. Hautes Étud. Sci. 82, 169-209 (1995; Zbl 0866.53029)] and by S. Barré [Ann. Inst. Fourier 45, No. 4, 1037-1059 (1995; Zbl 0831.53031)].

Reviewer: Gh.Pitiş (Braşov)

MSC:

53C20	Global Riemannian geometry, including pinching
53C22	Geodesics in global differential geometry

Keywords:

Hadamard space; ideal boundary; Tits metric

Citations:

Zbl 0866.53029; Zbl 0831.53031