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- W2067965535 abstract "0. Introduction. It is an interesting problem to investigate compactiίications of complete noncompact Riemannian manifolds. The ideal boundary of an Hadamard manifold Zis defined to be the set of equivalence classes of rays in X. Here the equivalence relation between two rays in X is obtained by an asymptotic relation between them. Busemann first defined (see [Bu, Chap. 3, §22]) an asymptotic relation between two rays (which he called co-ray relation and used to define parallelism on a straight G-space). This asymptotic relation is not symmetric in general and hence the equivalence classes of rays are not defined by it. If X is an Hadamard manifold, then this asymptotic relation becomes symmetric, and makes it possible to define the ideal boundary X(co) of X (see [EO] and [BGS]). Gromov defined in [BGS] the Tits metric on X{ao). Recently, Kause constructed an ideal boundary of an asymptotically nonnegatively curved manifold. The purpose of the present paper is, first of all, to define the ideal boundary M(oo) with the metric d^ as the set of natural equivalence classes of rays in a finitely connected, oriented, complete and noncompact surface M admitting total curvature. Then we investigate the geometry on the ideal boundary in terms of the total curvature. Here the total curvature c(M) of such a surface M is defined by an improper integral over M of the Gaussian curvature G:" @default.
- W2067965535 created "2016-06-24" @default.
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- W2067965535 date "1991-01-01" @default.
- W2067965535 modified "2023-09-24" @default.
- W2067965535 title "The ideal boundaries of complete open surfaces" @default.
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- W2067965535 doi "https://doi.org/10.2748/tmj/1178227534" @default.
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