19,857 research outputs found
Four-manifolds with positive curvature
In this note we prove that a four-dimensional compact oriented
half-confor\-mally flat Riemannian manifold is topologically
or provided that the sectional
curvatures all lie in the interval In addition,
we use the notion of biorthogonal (sectional) curvature to obtain a pinching
condition which guarantees that a four-dimensional compact manifold is
homeomorphic to a connected sum of copies of the complex projective plane or
the -sphere.Comment: Revised versio
Estimates for Minimal Volume and Minimal Curvature on 4-dimensional compact manifolds
In a remarkable article published in 1982, M. Gromov introduced the concept
of minimal volume, namely, the minimal volume of a manifold is defined to
be the greatest lower bound of the total volumes of with respect to
complete Riemannian metrics whose sectional curvature is bounded above in
absolute value by 1. While the minimal curvature, introduced by G. Yun in 1996,
is the smallest pinching of the sectional curvature among metrics of volume 1.
The goal of this article is to provide estimates to minimal volume and minimal
curvature on 4-dimensional compact manifolds involving some differential and
topological invariants. Among these ones, we get some sharp estimates for
minimal curvature.Comment: revised versio
Volume functional of compact -manifolds with a prescribed boundary metric
We prove that a critical metric of the volume functional on a -dimensional
compact manifold with boundary satisfying a second-order vanishing condition on
the Weyl tensor must be isometric to a geodesic ball in a simply connected
space form , or Moreover, we
provide an integral curvature estimate involving the Yamabe constant for
critical metrics of the volume functional, which allows us to get a rigidity
result for such critical metrics.Comment: To appear in The Journal of Geometric Analysi
Geometric Inequalities for Critical Metrics of the Volume Functional
The goal of this article is to investigate the geometry of critical metrics
of the volume functional on an -dimensional compact manifold with (possibly
disconnected) boundary. We establish sharp estimates to the mean curvature and
area of the boundary components of critical metrics of the volume functional on
a compact manifold. In addition, localized version estimates to the mean
curvature and area of the boundary of critical metrics are also obtained.Comment: Fixed typo
An Analogy of the Quantum Hall Condutivity in a Lorentz-symmetry Violation Setup
We investigated some influences of unconventional physics, such
Lorentz-symmetry violation, for quantum mechanical systems. In this context, we
calculated a important contribution for Standard Model Extension. In the
non-relativistic limit, we obtained a analogy of the Landau levels and the
quantum Hall conductivity related to this contribution for low energy systems.Comment: 12 pages, no figure
On Various Types of Shadowing for Geometric Lorenz Flows
We show that Lorenz flows have neither limit shadowing property nor average
shadowing property nor the asymptotic average shadowing property where the
reparametrizations related to these concepts relies on the set of increasing
homeomorphisms with bounded variation.Comment: 18 pages, 7 figure
Bach-flat critical metrics of the volume functional on 4-dimensional manifolds with boundary
The purpose of this article is to investigate Bach-flat critical metrics of
the volume functional on a compact manifold with boundary
Here, we prove that a Bach-flat critical metric of the volume functional on a
simply connected 4-dimensional manifold with boundary isometric to a standard
sphere must be isometric to a geodesic ball in a simply connected space form
or . Moreover, we show that in
dimension three the result even is true replacing the Bach-flat condition by
the weaker assumption that has divergence-free Bach tensor.Comment: To appear in The Journal of Geometric Analysi
Critical metrics of the volume functional on compact three-manifolds with smooth boundary
We study the space of smooth Riemannian structures on compact three-manifolds
with boundary that satisfies a critical point equation associated with a
boundary value problem, for simplicity, Miao-Tam critical metrics. We provide
an estimate to the area of the boundary of Miao-Tam critical metrics on compact
three-manifolds. In addition, we obtain a B\"ochner type formula which enables
us to show that a Miao-Tam critical metric on a compact three-manifold with
positive scalar curvature must be isometric to a geodesic ball in Comment: to appear in The Journal of Geometric Analysi
Bounds on volume growth of geodesic balls for Einstein warped products
The purpose of this note is to provide some volume estimates for Einstein
warped products similar to a classical result due to Calabi and Yau for
complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we
make use of the approach of quasi-Einstein manifolds which is directly related
to Einstein warped product. In particular, we present an obstruction for the
existence of such a class of manifolds.Comment: To appear in Proc. of the American Math. So
Lorentz symmetry violation and an Analog of Landau levels
Within the context of Lorentz violating extended electrodynamics, we study an
analog of Landau quantization for a system where a neutral particle moves in
the presence of an electromagnetic field and a constant four-vector that breaks
Lorentz symmetry. The nonrelativistic Hamiltonian associated to this system is
obtained using the Foldy-Wouthuysen transformation for a Dirac spinor. The
degenerated energy spectrum is obtained for a time-like and a space-like
parameter Lorentz-breaking vector. The energy dependence of the cyclotron
rotation direction in terms of supersymmetric quantum mechanics is analyzed.Comment: 11 pages, no figures, v2: new title,new versio
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