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.
Demonstratio Mathematica,
Journal Year:
2023,
Volume and Issue:
56(1)
Published: Jan. 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.
Filomat,
Journal Year:
2023,
Volume and Issue:
37(17), P. 5735 - 5749
Published: Jan. 1, 2023
In
this
paper,
the
relationships
between
geodesic
torsions,
normal
curvatures
and
of
parameter
curves
intersecting
at
any
angle
on
timelike
surfaces
in
Lorentz-Minkowski
3-
space
are
obtained
by
various
equations.
addition,
new
equivalents
well-known
formulas
(O.
Bonnet,
Euler,
Liouville)
found
space.
Finally,
examples
these
given.
Symmetry,
Journal Year:
2023,
Volume and Issue:
15(6), P. 1175 - 1175
Published: May 31, 2023
Ricci
solitons
(RS)
have
an
extensive
background
in
modern
physics
and
are
extensively
used
cosmology
general
relativity.
The
focus
of
this
work
is
to
investigate
almost
(RAS)
on
Lorentzian
manifolds
with
a
special
metric
connection
called
semi-symmetric
u-connection
(SSM-connection).
First,
we
show
that
any
quasi-Einstein
manifold
having
SSM-connection,
whose
RS,
Einstein
manifold.
A
similar
conclusion
also
holds
for
SSM-connection
admitting
RS
soliton
vector
Z
parallel
the
u.
Finally,
examine
gradient
(GRAS)
SSM-connection.
Mathematics,
Journal Year:
2023,
Volume and Issue:
11(11), P. 2516 - 2516
Published: May 30, 2023
The
method
of
gradient
estimation
for
the
heat-type
equation
using
Harnack
quantity
is
a
classical
approach
used
understanding
nature
solution
these
equations.
Most
studies
in
this
field
involve
Laplace–Beltrami
operator,
but
our
case,
we
studied
weighted
heat
that
involves
Laplacian.
This
produces
number
terms
involving
weight
function.
Thus,
article,
derive
estimate
positive
nonlinear
parabolic
on
Riemannian
manifold
evolving
under
geometric
flow.
Applying
estimation,
Li–Yau-type
and
Harnack-type
inequality
solution.
A
monotonicity
formula
entropy
functional
regarding
derived.
We
specify
results
various
different
flows.
Our
generalize
some
works.
AIMS Mathematics,
Journal Year:
2023,
Volume and Issue:
8(5), P. 11312 - 11324
Published: Jan. 1, 2023
<abstract><p>If
both
the
arc
length
and
intrinsic
curvature
of
a
curve
or
surface
are
preserved,
then
flow
is
said
to
be
inextensible.
The
absence
motion-induced
strain
energy
physical
characteristic
inextensible
flows.
In
this
paper,
we
study
tangential,
normal
binormal
ruled
surfaces
generated
by
with
constant
torsion,
which
also
called
Salkowski
curve.
We
investigate
whether
not
these
minimal
can
developed.
addition,
prove
some
theorems
related
within
three-dimensional
Euclidean
space.</p></abstract>
Symmetry,
Journal Year:
2023,
Volume and Issue:
15(4), P. 877 - 877
Published: April 6, 2023
In
this
paper,
we
improve
the
Chen
first
inequality
for
special
contact
slant
submanifolds
and
Legendrian
submanifolds,
respectively,
in
(α,β)
trans-Sasakian
generalized
Sasakian
space
forms
endowed
with
a
semi-symmetric
metric
connection.
Universe,
Journal Year:
2022,
Volume and Issue:
8(11), P. 595 - 595
Published: Nov. 11, 2022
In
this
article,
a
Ricci
soliton
and
*-conformal
are
examined
in
the
framework
of
trans-Sasakian
three-manifold.
beginning
paper,
it
is
shown
that
three-dimensional
manifold
type
(α,β)
admits
where
covariant
derivative
potential
vector
field
V
direction
unit
ξ
orthogonal
to
ξ.
It
also
demonstrated
if
structure
functions
meet
α2=β2,
then
constant
multiple
Furthermore,
nature
scalar
curvature
evolved
when
satisfies
soliton,
provided
α≠0.
Finally,
an
example
presented
verify
findings.
AIMS Mathematics,
Journal Year:
2023,
Volume and Issue:
8(12), P. 29042 - 29057
Published: Jan. 1, 2023
<abstract><p>The
purpose
of
the
article
is
to
analyze
behavior
spacetime
using
a
string
cloud
energy-momentum
tensor
$
\mathcal{T}
having
fluid
density
\rho
and
tension
\lambda
$,
named
<italic>relativistic
spacetime</italic>.
We
obtain
some
results
for
with
divergence-free
matter
diminishing
space
tensor.
Next,
we
discuss
curvature
characteristics,
such
as
conformally
flat,
Ricci
semi-symmetric
pseudo-Ricci-symmetric,
relativistic
spacetime.
In
addition,
gain
condition
that
coincides
equation
state
geometric
strings
in
spacetime.</p></abstract>
Symmetry,
Journal Year:
2023,
Volume and Issue:
15(4), P. 910 - 910
Published: April 14, 2023
In
this
work,
we
present
a
new
Bishop
frame
for
the
conjugate
curve
of
in
3-dimensional
Lie
group
G3.
With
help
frame,
derive
parametric
representation
sweeping
surface
and
show
that
curves
on
are
curvature
lines.
We
then
examine
local
singularities
convexity
establish
sufficient
necessary
conditions
it
to
be
developable
ruled
surface.
Additionally,
provide
detailed
explanations
examples
its
applications.
