Open AccessGeodesic completeness of the left-invariant metrics on ℝ H n
Author(s) -
Srdjan Vukmirović,
Tijana Šukilović
Publication year - 2020
Publication title -
ukrains’kyi matematychnyi zhurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v72i5.645
Subject(s) - geodesic , invariant (physics) , mathematics , mathematical analysis , mathematical physics
UDC 514We give the full classification of left-invariant metrics of an arbitrary signature on the Lie group corresponding to the real hyperbolic space. We show that all metrics have constant sectional curvature and that they are geodesically complete only in the Riemannian case.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom