A new approach to special curved surface families according to modified orthogonal frame
AIMS Mathematics,
Journal Year:
2024,
Volume and Issue:
9(8), P. 20662 - 20676
Published: Jan. 1, 2024
The
main
purpose
of
this
paper
was
to
investigate
the
problem
finding
surface
family
with
respect
two
different
types
modified
orthogonal
frames
defined
for
curves
curvature
and
torsion
from
zero,
respectively.
For
purpose,
conditions
were
given
parametric
curve
frame
in
three-dimensional
Euclidean
space
be
a
geodesic,
asymptotic
or
line
on
surface,
It
has
been
shown
that
member
same
special
such
as
asymptotic,
can
obtained
by
choosing
deviation
functions
writing
satisfy
conditions.
Finally,
several
examples
support
study.
Language: Английский
Bertrand Offsets of Slant Ruled Surfaces in Euclidean 3-Space
Symmetry,
Journal Year:
2024,
Volume and Issue:
16(2), P. 235 - 235
Published: Feb. 15, 2024
In
this
paper,
we
investigate
and
specify
the
Bertrand
offsets
of
slant
ruled
developable
surfaces
in
Euclidean
3-space
E3.
This
is
accomplished
by
utilizing
symmetry
curves.
As
a
consequence
this,
present
parameterization
for
any
surfaces.
addition
to
monarchies
these
assign
them
their
own
unique
classification.
Also,
illustrate
some
examples
Language: Английский
A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space
Symmetry,
Journal Year:
2023,
Volume and Issue:
15(11), P. 1986 - 1986
Published: Oct. 27, 2023
The
main
outcome
of
this
work
is
the
construction
a
surface
pencil
with
similarity
to
Bertrand
curves
in
Euclidean
3-space
E3.
Then,
by
exploiting
Serret–Frenet
frame,
we
deduce
sufficient
and
necessary
conditions
for
as
joint
curvature
lines.
Consequently,
expansion
ruled
also
designed.
As
demonstrations
our
essential
findings,
illustrate
some
models
emphasize
process.
Language: Английский
Timelike surfaces with Bertrand geodesic curves in Minkowski 3–space
AIP Advances,
Journal Year:
2024,
Volume and Issue:
14(7)
Published: July 1, 2024
Geodesic
curves
on
a
surface
play
an
essential
role
in
reasonable
implementation.
A
curve
is
geodesic
if
its
principal
normal
vector
aligned
with
the
normal.
Using
Serret–Frenet
frame,
timelike
(TL)
surfaces
can
be
specified
as
linear
combinations
of
components
local
frames
Minkowski
3–space
E13.
With
these
parametric
representations,
we
obtained
indispensable
and
required
events
for
Bertrand
(B)
to
surfaces.
Afterword,
conclusion
regarding
TL
ruled
also
made.
Finally,
models
are
declared
assure
that
suggested
methods
effective
outcome
manufacturing
by
modifying
styles
pair.
Language: Английский
Slant spacelike ruled surfaces and their Bertrand offsets
Frontiers in Physics,
Journal Year:
2024,
Volume and Issue:
12
Published: Dec. 5, 2024
In
this
work,
we
investigate
the
synthesis
problem
of
slant
spacelike
ruled
surfaces
and
associated
Bertrand
offsets
(BO)
in
id="m2">E13
(Minkowsk
3-space).
We
provide
parametric
equation
for
a
non-developable
surface
id="m3">SLRSFS
Therefore,
found
appropriate
id="m6">
Language: Английский