Helixes on Clifford surfaces in a hyperbolic space H^3 of positive curvature are investigated. We formulate the following facts for a Clifford surface of every type in the space H^3. A curve on a Clifford surface of the space H^3 is a helix if and only if it is a loxodrome. If a helix ξ on a Clifford surface of the space H^3 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 H^3 are poles of each loxodrome on this surface.

1.
N. V.
Efimov
,
Higher Geometry
(
FIZMATLIT
,
Moscow
,
1971
), pp.
376
392
.
2.
F.
Klein
,
Vorlesungen Über Nicht-Euclidische Geometrie
(
Verlag von Julius Springer
,
Berlin
,
1928
).
3.
B. A.
Rosenfeld
,
Non-Euclidean spaces
(
Nauka
,
Moscow
,
1969
).
4.
W.
DeSitter
,
Proc. Royal Acad. Amsterdam
19
(
2
),
1217
1225
(
1917
).
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.
L. N.
Romakina
,
Chebyshevskii Sb.
16
(
2
),
208
221
(
2015
).
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.
L. N.
Romakina
,
Journal for Geometry and Graphics
20
(
2
),
209
224
(
2016
).
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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