|
Proper Helix of
Order 6 And
LC Helix in
Pseudo-Euclidean
Space E84
Buddhadev Pal (1) and Santosh Kumar (2)
(1,2) Department
of Mathematics,
Institute of
Science, Banaras
Hindu
University,
Varanasi-221005,
India
Email address:
(1)
pal.buddha@gmail.com
Email address:
(2)
thakursantoshbhu@gmail.com
Doi :
https://doi.org/10.47013/15.4.19
Cited by :
Jordan J. Math &
Stat.,
15 (4B) (2022),
1077 - 1092
PDF
Received on:
Oct. 21,
2021;
Accepted
on: April 14,
2022
Abstract. In this
paper, we used
the result that
complex
hyperbolic
spaces CH2
(−4c/3) with
holomorphic
sectional
curvature −4c/3
are
isometrically
embedded in E84
. By considering
a circle in CH2(−4c/3),
we prove that
the image of the
circle by
isometric
embedding is a
proper helix of
order 6 in E84.
Moreover, we
define a
generalized LC
helix on a
submanifold of E84.
Also, we show
that the image
of a circle by
isometric
embedding from
complex
hyperbolic plane
CH2(−4c/3)
to
pseudo-Euclidean
space E84
is a generalized
LC helix on some
submanifold of E84.
Keywords: Curve of proper
order, complex
hyperbolic
space,
generalized LC
helix, isometric
embedding,
parallel second
fundamental
form.
|
