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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 1, Pages 3–14 (Mi ivm9065)  

This article is cited in 1 scientific paper (total in 1 paper)

Geometry of tangent cone to $G$-space of nonpositive curvature with distinguished family of segments

P. D. Andreev, V. V. Starostina

Chair of Mathematical Analysis, Algebra and Geometry, Northern (Arctic) Federal University, 17 Severnoi Dviny Embankment, Arkhangelsk, 163002 Russia

Abstract: We study a construction of the tangent cone for Busemann $G$-space with distinguished family of segments with additional condition of Busemann curvature nonpositivity. We prove that the constructed cone has geometric properties analogous to the properties of the tangent cone of the standard $G$-space of nonpositive curvature. Earlier the tangent cone construction was used by the first author for proving H. Busemann's conjecture for $G$-spaces of nonpositive curvature stating that every such space is a topological manifold. The constructed tangent cone can be considered as a main tool for the generalization of this theorem to the presented class of spaces.

Keywords: Busemann $G$-space, distinguished family of segments family, nonpositive curvature, Busemann conjecture, tangent cone.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00219-a


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:1, 1–10

Bibliographic databases:

UDC: 514.1
Received: 27.05.2014

Citation: P. D. Andreev, V. V. Starostina, “Geometry of tangent cone to $G$-space of nonpositive curvature with distinguished family of segments”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 1, 3–14; Russian Math. (Iz. VUZ), 60:1 (2016), 1–10

Citation in format AMSBIB
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\by P.~D.~Andreev, V.~V.~Starostina
\paper Geometry of tangent cone to $G$-space of nonpositive curvature with distinguished family of segments
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 1
\pages 3--14
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\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 1
\pages 1--10
\crossref{https://doi.org/10.3103/S1066369X16010011}
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    This publication is cited in the following articles:
    1. P. D. Andreev, V. V. Starostina, “Normirovannye ploskosti v kasatelnom konuse k khordovomu prostranstvu nepolozhitelnoi krivizny”, Izv. vuzov. Matem., 2019, no. 1, 3–17  mathnet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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