Ruled Surfaces of Adjoint Curve with the Modified Orthogonal Frame
Journal of New Theory,
Год журнала:
2024,
Номер
49, С. 69 - 82
Опубликована: Дек. 31, 2024
This
paper
analyzes
several
specific
ruled
surfaces
generated
by
the
base
curve
$\alpha$
and
its
director
or
$\alpha$'s
adjoint
$\beta$
curve,
where
curves
are
frame
vectors
of
modified
orthogonal
in
$E^{3}$.
Furthermore,
this
studies
flat
minimal
properties
surfaces,
as
well
their
asymptotic
geodesic
curves.
Afterward,
it
exemplifies
theoretical
results
herein.
Finally,
discusses
need
for
further
research.
Язык: Английский
On the curve evolution with a new modified orthogonal Saban frame
AIMS Mathematics,
Год журнала:
2024,
Номер
9(10), С. 29573 - 29586
Опубликована: Янв. 1, 2024
<p>The
flow
of
a
curve
is
said
to
be
inextensible
if
the
arc
length
in
first
case
and
intrinsic
curvature
second
are
preserved.
In
this
work,
we
investigated
on
$
S^2
according
modified
orthogonal
Saban
frame.
Initially,
gave
definition
frame
then
established
relations
between
Frenet
frames.
Later,
determined
geodesic
unit
sphere
using
Also,
some
theorems
results
for
special
cases
evolution
sphere.
Finally,
examples
their
graphs
equation
curvatures.</p>
Язык: Английский