AIMS Mathematics,
Год журнала:
2024,
Номер
9(4), С. 9867 - 9883
Опубликована: Янв. 1, 2024
<abstract><p>In
this
treatise,
several
relationships
are
improved
for
the
axodes
of
one-parameter
spatial
movements.
Results
devised
in
some
theorems
which
characterize
many
kinematical
and
geometrical
properties
movements
employing
data
stationary
movable
axodes.
An
example
illustrates
application
formulae
derived.
Our
findings
contribute
to
a
greater
understanding
similarities
between
axodes,
with
possible
applications
fields
such
as
mechanical
engineering.</p></abstract>
Symmetry,
Год журнала:
2023,
Номер
15(5), С. 976 - 976
Опубликована: Апрель 25, 2023
In
this
article,
we
derived
an
equality
for
CR-warped
product
in
a
complex
space
form
which
forms
the
relationship
between
gradient
and
Laplacian
of
warping
function
second
fundamental
form.
We
necessary
conditions
submanifolds
Ka¨hler
manifold
to
be
Einstein
impact
Ricci
soliton.
Some
classification
by
using
Euler–Lagrange
equation,
Dirichlet
energy
Hamiltonian
is
given.
also
derive
some
characterizations
warped
manifolds
under
Curvature
Divergence
Hessian
tensor.
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.
AIMS Mathematics,
Год журнала:
2023,
Номер
8(8), С. 17335 - 17353
Опубликована: Янв. 1, 2023
<abstract><p>Let
$
(M,
g)
be
an
n
$-dimensional
(pseudo-)Riemannian
manifold
and
TM
its
tangent
bundle
equipped
with
the
complete
lift
metric
^{C}g
$.
First,
we
define
a
Ricci
quarter-symmetric
connection
\overline{\nabla
}
on
Second,
compute
all
forms
of
curvature
tensors
study
their
properties.
We
also
mean
gradient
solitons
are
important
topics
studied
extensively
lately.
Necessary
sufficient
conditions
for
to
become
soliton
concerning
presented.
Finally,
search
locally
conformally
flat
respect
$.</p></abstract>
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>
Mathematics,
Год журнала:
2023,
Номер
11(15), С. 3365 - 3365
Опубликована: Авг. 1, 2023
The
characterization
of
Finsler
spaces
with
Ricci
curvature
is
an
ancient
and
cumbersome
one.
In
this
paper,
we
have
derived
expression
for
the
homogeneous
generalized
Matsumoto
change.
Moreover,
deduced
aforementioned
space
vanishing
S-curvature.
These
findings
contribute
significantly
to
understanding
complex
nature
their
properties.
Mathematics,
Год журнала:
2023,
Номер
11(15), С. 3427 - 3427
Опубликована: Авг. 7, 2023
We
present
a
family
of
hypersurfaces
revolution
distinguished
by
four
parameters
in
the
five-dimensional
pseudo-Euclidean
space
E25.
The
matrices
corresponding
to
fundamental
form,
Gauss
map,
and
shape
operator
this
are
computed.
By
utilizing
Cayley–Hamilton
theorem,
we
determine
curvatures
specific
family.
Furthermore,
establish
criteria
for
maximality
within
framework.
Additionally,
reveal
relationship
between
Laplace–Beltrami
5×5
matrix.
Axioms,
Год журнала:
2023,
Номер
12(5), С. 486 - 486
Опубликована: Май 17, 2023
In
this
article,
we
examine
the
relationship
between
Darboux
frames
along
parameter
curves
and
frame
of
base
curve
ruled
surface.
We
derive
equations
quaternionic
shape
operators,
which
can
rotate
tangent
vectors
around
normal
vector,
find
corresponding
rotation
matrices.
Using
these
Gauss
curvature
mean
explore
how
properties
are
found
by
use
Frenet
instead
generator
vectors.
provide
illustrative
examples
to
better
demonstrate
concepts
results
discussed.
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.
Abstract
The
prime
objective
of
the
approach
is
to
give
geometric
classifications
k
k
-almost
Ricci
solitons
associated
with
paracontact
manifolds.
Let
M2n+1(φ,ξηg)
{M}^{2n+1}\left(\varphi
,\xi
,\eta
,g)
be
a
metric
manifold,
and
if
K
K
-paracontact
g
represents
soliton
Vλ
\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
