On the curvatures of timelike circular surfaces in Lorentz-Minkowski space
Filomat,
Год журнала:
2024,
Номер
38(4), С. 1423 - 1437
Опубликована: Янв. 1, 2024
In
this
paper,
using
the
classical
methods
of
differential
geometry,
wedefine
invariants
timelike
circular
surfaces
in
Lorentz-Minkowski
space
R3
1,
called
curvature
functions,
and
show
kinematic
meaning
these
invariants.
Then
we
discuss
properties
give
a
kind
classification
with
theories
Besides,
to
demonstrate
our
theoretical
results
some
computational
examples
are
given
plotted.
Язык: Английский
On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space
AIMS Mathematics,
Год журнала:
2023,
Номер
8(9), С. 22256 - 22273
Опубликована: Янв. 1, 2023
<abstract><p>In
this
study,
the
partner-ruled
surfaces
in
Minkowski
3-space,
which
are
defined
according
to
Frenet
vectors
of
non-null
space
curves,
introduced
with
extra
conditions
that
guarantee
existence
definite
surface
normals.
First,
requirements
each
pair
be
simultaneously
developable
and
minimal
(or
maximal
for
spacelike
surfaces)
investigated.
The
also
characterize
asymptotic,
geodesic
curvature
lines
parameter
curves
these
surfaces.
Finally,
study
provides
examples
timelike
includes
their
graphs.</p></abstract>
Язык: Английский
Kinematic-geometry of a line trajectory and the invariants of the axodes
Demonstratio Mathematica,
Год журнала:
2023,
Номер
56(1)
Опубликована: Янв. 1, 2023
Abstract
In
this
article,
we
investigate
the
relationships
between
instantaneous
invariants
of
a
one-parameter
spatial
movement
and
local
axodes.
Specifically,
provide
new
proofs
for
Euler-Savary
Disteli
formulas
using
E.
Study
map
in
kinematics,
showcasing
its
elegance
efficiency.
addition,
introduce
two
line
congruences
thoroughly
analyze
their
equivalence.
Our
findings
contribute
to
deeper
understanding
interplay
movements
axodes,
with
potential
applications
fields
such
as
robotics
mechanical
engineering.
Язык: Английский
Geometric classifications of k-almost Ricci solitons admitting paracontact metrices
Open Mathematics,
Год журнала:
2023,
Номер
21(1)
Опубликована: Янв. 1, 2023
Abstract
The
prime
objective
of
the
approach
is
to
give
geometric
classifications
k
k
-almost
Ricci
solitons
associated
with
paracontact
manifolds.
Let
M
2
n
+
1
(
φ
,
ξ
η
g
)
{M}^{2n+1}\left(\varphi
,\xi
,\eta
,g)
be
a
metric
manifold,
and
if
K
K
-paracontact
g
represents
soliton
V
λ
\left(g,V,k,\lambda
)
potential
vector
field
V
Jacobi
along
Reeb
\xi
,
then
either
=
−
k=\lambda
-2n
or
-Ricci
soliton.
Next,
we
consider
manifold
as
infinitesimal
transformation
collinear
.
We
have
proved
that
non-zero
operator
Q
Q
commutes
structure
\varphi
it
Einstein
constant
scalar
curvature
equals
-2n\left(2n+1)
Finally,
deduced
para-Sasakian
admitting
gradient
Язык: Английский
Homology of Warped Product Semi-Invariant Submanifolds of a Sasakian Space Form with Semisymmetric Metric Connection
Journal of Mathematics,
Год журнала:
2023,
Номер
2023, С. 1 - 8
Опубликована: Окт. 10, 2023
This
paper
focuses
on
the
investigation
of
semi-invariant
warped
product
submanifolds
Sasakian
space
forms
endowed
with
a
semisymmetric
metric
connection.
We
delve
into
study
these
and
derive
several
fundamental
results.
Additionally,
we
explore
practical
implications
our
findings
by
applying
them
to
homology
analysis
submanifolds.
Notably,
present
proof
demonstrating
absence
stable
currents
for
under
specific
condition.
Язык: Английский
A helicoidal hypersurfaces family in five-dimensional euclidean space
Filomat,
Год журнала:
2024,
Номер
38(11), С. 3813 - 3824
Опубликована: Янв. 1, 2024
A
family
of
helicoidal
hypersurfaces,
denoted
as
x(u,v,s,t),
is
introduced
within
the
context
five-dimensional
Euclidean
space
E5.
Matrices
for
first
and
second
fundamental
forms,
Gauss
map,
shape
operator
matrix
x
are
derived.
Furthermore,
by
employing
Cayley?Hamilton
theorem
to
define
curvatures
these
computed
specifically
hypersurfaces
x.
Several
relationships
between
mean
Gauss?Kronecker
established.
Additionally,
equation
?x
=
Ax
demonstrated,
where
a
5
?
in
Язык: Английский