Horo-tightness and total (absolute) curvatures in hyperbolic spaces

G. Solanes; E. Teufel

doi:10.1007/s11856-012-0099-8

Horo-tightness and total (absolute) curvatures in hyperbolic spaces

G. Solanes, E. Teufel

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

We prove Gauß-Bonnet-type and Chern-Lashof-type formulas for immersions in hyperbolic space. Moreover we investigate the notion of tightness with respect to horospheres introduced by T. E. Cecil and P. J. Ryan. We introduce the notions of top-set and drop-set, and we prove fundamental properties of horo-tightness in hyperbolic spaces. © 2012 Hebrew University Magnes Press.

Original language	English
Pages (from-to)	427-459
Journal	Israel Journal of Mathematics
Volume	194
Issue number	1
DOIs	https://doi.org/10.1007/s11856-012-0099-8
Publication status	Published - 1 Mar 2013

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Solanes, G., & Teufel, E. (2013). Horo-tightness and total (absolute) curvatures in hyperbolic spaces. Israel Journal of Mathematics, 194(1), 427-459. https://doi.org/10.1007/s11856-012-0099-8

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AB - We prove Gauß-Bonnet-type and Chern-Lashof-type formulas for immersions in hyperbolic space. Moreover we investigate the notion of tightness with respect to horospheres introduced by T. E. Cecil and P. J. Ryan. We introduce the notions of top-set and drop-set, and we prove fundamental properties of horo-tightness in hyperbolic spaces. © 2012 Hebrew University Magnes Press.

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