Abstract
In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In particular, we prove that both properties characterize the non-positivity of the sectional curvature on Riemannian manifolds. Further results are also established on reversible/non-reversible Finsler-Minkowski spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 602-610 |
| Number of pages | 9 |
| Journal | Differential Geometry and its Application |
| Volume | 31 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Oct 2013 |
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Keywords
- Alexandrov NPC space
- Busemann NPC space
- Curvature
- Metric projection
- Minkowski space
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Analysis
- Geometry and Topology
Cite this
Metric projections versus non-positive curvature. / Kristály, A.; Repovš, Dušan.
In: Differential Geometry and its Application, Vol. 31, No. 5, 10.2013, p. 602-610.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Metric projections versus non-positive curvature
AU - Kristály, A.
AU - Repovš, Dušan
PY - 2013/10
Y1 - 2013/10
N2 - In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In particular, we prove that both properties characterize the non-positivity of the sectional curvature on Riemannian manifolds. Further results are also established on reversible/non-reversible Finsler-Minkowski spaces.
AB - In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In particular, we prove that both properties characterize the non-positivity of the sectional curvature on Riemannian manifolds. Further results are also established on reversible/non-reversible Finsler-Minkowski spaces.
KW - Alexandrov NPC space
KW - Busemann NPC space
KW - Curvature
KW - Metric projection
KW - Minkowski space
UR - http://www.scopus.com/inward/record.url?scp=84879329964&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879329964&partnerID=8YFLogxK
U2 - 10.1016/j.difgeo.2013.06.002
DO - 10.1016/j.difgeo.2013.06.002
M3 - Article
AN - SCOPUS:84879329964
VL - 31
SP - 602
EP - 610
JO - Differential Geometry and its Applications
JF - Differential Geometry and its Applications
SN - 0926-2245
IS - 5
ER -