Mathematics,
Journal Year:
2023,
Volume and Issue:
11(20), P. 4281 - 4281
Published: Oct. 13, 2023
We
obtain
some
generalized
Minkowski
type
integral
formulas
for
compact
Riemannian
(resp.,
spacelike)
hypersurfaces
in
Lorentzian)
manifolds
the
presence
of
an
arbitrary
vector
field
that
we
assume
to
be
timelike
case
where
ambient
space
is
Lorentzian.
Some
these
generalize
existing
conformal
and
Killing
fields.
apply
interesting
results
concerning
characterization
such
particular
cases
as
when
Einstein
admitting
(in
particular,
or
Killing)
field,
hypersurface
has
a
constant
mean
curvature.
Mathematics,
Journal Year:
2023,
Volume and Issue:
11(23), P. 4717 - 4717
Published: Nov. 21, 2023
This
study
establishes
new
upper
bounds
for
the
mean
curvature
and
constant
sectional
on
Riemannian
manifolds
first
positive
eigenvalue
of
q-Laplacian.
In
particular,
various
estimates
are
provided
q-Laplace
operator
closed
orientated
(l+1)-dimensional
special
contact
slant
submanifolds
in
a
Sasakian
space
form,
M˜2k+1(ϵ),
with
ψ1-sectional
curvature,
ϵ.
From
our
main
results,
we
recovered
Reilly-type
inequalities,
which
were
proven
before
this
study.
Symmetry,
Journal Year:
2024,
Volume and Issue:
16(1), P. 95 - 95
Published: Jan. 11, 2024
The
primary
objective
of
this
paper
is
to
explore
contact
CR-warped
product
submanifolds
Sasakian
space
forms
equipped
with
a
semi-symmetric
metric
connection.
We
thoroughly
examine
these
and
establish
various
key
findings.
Furthermore,
we
derive
an
inequality
relating
the
Ricci
curvature
mean
vector
warping
function.
Mathematical Methods in the Applied Sciences,
Journal Year:
2024,
Volume and Issue:
47(11), P. 8626 - 8637
Published: March 12, 2024
In
this
paper,
we
generalize
the
main
ideas
and
statements
of
theory
infinitesimal
bending
in
Euclidean
3‐space
to
dual
curves
.
The
basic
condition
introduce
is
invariance
arc
length
with
appropriate
precision.
Necessary
sufficient
conditions
for
field
be
an
are
given.
Some
useful
formulas
facts
about
obtained.
An
explicit
characterization
spherical
curve
presented,
corresponding
decomposed
into
vectors
Frenet
frame.
Finally,
some
examples
given
illustrate
our
results.
Modern Physics Letters A,
Journal Year:
2024,
Volume and Issue:
39(10)
Published: March 28, 2024
We
give
a
method
for
constructing
generalized
null
Cartan
helices,
which
may
have
singularities,
by
using
regular
space-like
plane
curves
and
smooth
functions
in
Minkowski
3-space.
also
study
the
principle
normal
worldsheet,
is
deeply
related
to
helices
from
viewpoint
of
singularity
theory.
Axioms,
Journal Year:
2023,
Volume and Issue:
12(12), P. 1078 - 1078
Published: Nov. 24, 2023
This
paper
investigates
singly
warped
product
manifolds
admitting
semi-conformal
curvature
tensors.
The
form
of
the
Riemann
tensor
and
Ricci
base
fiber
a
semi-conformally
flat
manifold
are
provided.
It
is
demonstrated
that
has
constant
curvature.
Sufficient
requirements
on
warping
function
to
ensure
quasi-Einstein
or
an
Einstein
Symmetry,
Journal Year:
2024,
Volume and Issue:
16(2), P. 190 - 190
Published: Feb. 6, 2024
The
main
goal
of
this
research
paper
is
to
investigate
contact
CR-warped
product
submanifolds
within
Sasakian
space
forms,
utilizing
a
semi-symmetric
metric
connection.
We
conduct
comprehensive
analysis
these
and
establish
several
significant
results.
Additionally,
we
formulate
an
inequality
that
establishes
relationship
between
the
squared
norm
second
fundamental
form
warping
function.
Lastly,
present
number
geometric
applications
derived
from
our
findings.
Filomat,
Journal Year:
2024,
Volume and Issue:
38(11), P. 3813 - 3824
Published: Jan. 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
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(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.
Axioms,
Journal Year:
2023,
Volume and Issue:
12(11), P. 1022 - 1022
Published: Oct. 30, 2023
A
principal
curve
on
a
surface
plays
paramount
role
in
reasonable
implementations.
is
if
its
tangents
are
directions.
Using
the
Serret–Frenet
frame,
pencil
couple
can
be
expressed
as
linear
combinations
of
components
local
frames
Galilean
3-space
G3.
With
these
parametric
representations,
family
surfaces
using
curves
(curvature
lines)
constructed,
and
necessary
sufficient
condition
for
given
Bertrand
to
derived
our
approach.
Moreover,
satisfy
geodesic
requirements
also
analyzed.
As
implementations
main
consequences,
we
expound
upon
some
models
confirm
method.
