Helixes on Clifford surfaces in a hyperbolic space of positive curvature are investigated. We formulate the following facts for a Clifford surface of every type in the space . A curve on a Clifford surface of the space is a helix if and only if it is a loxodrome. If a helix ξ on a Clifford surface of the space contains opposite vertices of the coordinate rectangle of the basic coordinate network, then the helix ξ divides this coordinate rectangle into two parts of equal areas. The absolute points of the hyperbolic axis of a Clifford surface in the space are poles of each loxodrome on this surface.
REFERENCES
1.
2.
F.
Klein
, Vorlesungen Über Nicht-Euclidische Geometrie
(Verlag von Julius Springer
, Berlin
, 1928
).3.
4.
5.
H. S. M.
Coxeter
, Amer. Math. Mon.
50
(4
), 217
–228
(1943
).6.
L. N.
Romakina
, “Development of ideas about the geometry of the surrounding space
,” in Effective researches of modernity
, Scientific articles collection of the International Scientific Conferences of Eurasian Scientific Association 10
(ESA
, Moscow
, 2015
), pp. 18
–21
.7.
L. N.
Romakina
, Geometry of the hyperbolic plane of positive curvature. P. 1: Trigonometry
(Publishing House of the Saratov University
, Saratov
, 2013
).8.
L. N.
Romakina
, Publications de L’Institut Mathem. Nouvelle serie
99
(113
), 139
–1548
(2016
).9.
10.
L. N.
Romakina
, Geometries of the co-Euclidean and co-pseudoeuclidean planes
(Scientific book
, Saratov
, 2008
).11.
L. N.
Romakina
, International Electronic Journal of Geometry
9
(2
), 50
–58
(2016
).12.
L. N.
Romakina
, “The volume of a monopolar tetrahedron in a hyperbolic space of positive curvature
,” in Strategies for stable development of world science
, Scientific articles collection of the International Scientific Conferences of Eurasian Scientific Association
5
(27
) (ESA
, Moscow
, 2017
), pp. 27
–30
.13.
L. N.
Romakina
, Proceedings of the International Geometry Center
10
(2
), 56
–71
(2017
).14.
L. N.
Romakina
, “Clifford surfaces in a hyperbolic space of positive curvature
,” in Strategies for stable development of world science
, Scientific articles collection of the International Scientific Conferences of Eurasian Scientific Association
5
(27
) (ESA
, Moscow
, 2017
), pp. 30
–33
.15.
L. N.
Romakina
, Geometry of the hyperbolic plane of positive curvature. P. 2:Transformations and simple partitions
(Publishing House of the Saratov University
, Saratov
, 2013
).16.
L. N.
Romakina
, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
12
(3
), 37
–44
(2012
).17.
L. N.
Romakina
, Journal of Mathematical Sciences
212
(5
), 605
–621
(2016
).18.
19.
L. N.
Romakina
, “Method of visualization of figures near infinity,” in Mathematical methods and information technologies of management in science, education and the law-enforcement sphere
, edited by V. A.
Minaev
(Academy of the FPS of Russia
, Ryazan
, 2017
), pp. 321
–323
.20.
L. N.
Romakina
, Sbornik: Mathematics
203
(9
), 1310
–1341
(2012
).
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