Symmetry,
Journal Year:
2023,
Volume and Issue:
15(10), P. 1841 - 1841
Published: Sept. 28, 2023
In
this
manifestation,
we
explain
the
geometrisation
of
η-Ricci–Yamabe
soliton
and
gradient
on
Riemannian
submersions
with
canonical
variation.
Also,
prove
any
fiber
same
submersion
variation
(in
short
CV)
is
an
soliton,
which
called
solitonic
fiber.
under
setting,
inspect
in
a
φ(Q)-vector
field.
Moreover,
provide
example
submersions,
illustrates
our
findings.
Finally,
explore
some
applications
along
cohomology,
Betti
number,
Pontryagin
classes
number
theory.
Symmetry,
Journal Year:
2023,
Volume and Issue:
15(2), P. 277 - 277
Published: Jan. 19, 2023
In
this
paper,
we
consider
the
singularities
and
geometrical
properties
of
timelike
developable
surfaces
with
Bishop
frame
in
Minkowski
3-space.
Taking
advantage
singularity
theory,
give
classification
generic
these
surfaces.
Furthermore,
an
example
application
is
given
to
illustrate
applications
results.
AIMS Mathematics,
Journal Year:
2023,
Volume and Issue:
8(6), P. 13875 - 13888
Published: Jan. 1, 2023
<abstract><p>In
this
paper,
we
study
the
singularities
on
a
non-developable
ruled
surface
according
to
Blaschke's
frame
in
Euclidean
3-space.
Additionally,
prove
that
singular
points
occur
kind
of
and
use
singularity
theory
technique
examine
these
singularities.
Finally,
construct
an
example
confirm
demonstrate
our
primary
finding.</p></abstract>
Symmetry,
Journal Year:
2023,
Volume and Issue:
15(1), P. 173 - 173
Published: Jan. 6, 2023
The
approach
of
the
paper
is
on
spacelike
circular
surfaces
in
Minkowski
3-space.
A
surface
a
one-parameter
family
Lorentzian
circles
with
fixed
radius
regarding
non-null
curve,
which
acts
as
spine
and
it
has
symmetrical
properties.
In
study,
we
have
parametrized
provided
their
geometric
singularity
properties
such
Gaussian
mean
curvatures,
comparing
them
those
ruled
classification
singularities.
Furthermore,
conditions
for
roller
coaster
to
be
flat
or
minimal
are
obtained.
Meanwhile,
support
results
some
examples.
Mathematical Methods in the Applied Sciences,
Journal Year:
2023,
Volume and Issue:
46(9), P. 11157 - 11171
Published: March 2, 2023
In
this
paper,
we
mainly
investigate
(contra)pedals
and
(anti)orthotomics
of
frontals
in
the
de
Sitter
2‐space
from
viewpoint
singularity
theory
differential
geometry.
We
utilize
Legendrian
Frenet
frames
to
provide
parametric
representations
(contra)pedal
curves
spacelike
timelike
geometric
properties
these
curves.
then
introduce
orthotomics
explain
as
wavefronts
theory.
Furthermore,
generalize
methods
study
antiorthotomics
2‐space.
Symmetry,
Journal Year:
2023,
Volume and Issue:
15(5), P. 976 - 976
Published: April 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.
AIMS Mathematics,
Journal Year:
2023,
Volume and Issue:
8(8), P. 17335 - 17353
Published: Jan. 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,
Journal Year:
2023,
Volume and Issue:
8(9), P. 22256 - 22273
Published: Jan. 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>
Axioms,
Journal Year:
2023,
Volume and Issue:
12(5), P. 486 - 486
Published: May 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.
AIMS Mathematics,
Journal Year:
2023,
Volume and Issue:
8(7), P. 16278 - 16290
Published: Jan. 1, 2023
<abstract><p>In
this
paper,
we
investigate
Zermelo's
navigation
problem
for
some
special
rotation
surfaces.
In
respect,
find
Randers-type
metrics
these
Furthermore,
get
the
H-distortion
metric
induced
by
surfaces.</p></abstract>
