-non-degenerate spaces are spacetimes that can be characterized uniquely by their scalar curvature invariants. The ultimate goal of the current work is to construct a basis for the scalar polynomial curvature invariants in three dimensional Lorentzian spacetimes. In particular, we seek a minimal set of alg…
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48 results for “scalar curvature invariants”
The paper explores Kähler-like metrics on generalized flag manifolds.
problem Finding invariant almost Hermitian structures with specific scalar curvature properties.
method Investigating invariant almost Hermitian geometry on generalized flag manifolds, focusing on Kähler-like metrics.
result Examples of Kähler-like metrics satisfying are provided.
The paper explores constant holomorphic d-scalar curvature on specific manifolds.
problem Existence and prescription of constant holomorphic d-scalar curvature.
method Study of closed, connected almost Hermitian manifolds of dimension .
result Obtained an application and variation formula for a conformal invariant.
Study adds scalar curvatures of mapped manifolds to Riemannian products.
problem Additivity of scalar curvatures in Riemannian products.
method Stabilized scalar curvatures of mapped manifolds.
result Proves additivity in some cases.
In this paper, we use localization algebras to study higher rho invariants of closed spin manifolds with positive scalar curvature metrics. The higher rho invariant is a secondary invariant and is closely related to positive scalar curvature problems. The main result of the paper connects the higher index of the Dirac …
The paper classifies flag manifolds with specific isotropy components and finds conditions for Kähler-like scalar curvature.
problem Classifying flag manifolds with specific isotropy components and finding conditions for Kähler-like scalar curvature.
method Investigating invariant almost Hermitian structures on generalized flag manifolds with two or three irreducible components.
result Classification of flag manifolds admitting Kähler-like scalar curvature and conditions for such structures.
Conformally variational Riemannian invariants (CVIs), such as the scalar curvature, are homogeneous scalar invariants which arise as the gradient of a Riemannian functional. We establish a wide range of stability and rigidity results involving CVIs, generalizing many such results for the scalar curvature.
This note is a study of nonnegativity conditions on curvature which are preserved by the Ricci flow. We focus on specific kinds of curvature conditions which we call noncoercive, these are the conditions for which nonnegative curvature and vanishing scalar curvature doesn't imply flatness. We show that, in dimensions g…
Explains peculiarities of 4D scalar curvature via Yamabe invariant.
problem Interplay between scalar curvature and differential topology in 4-manifolds.
method Careful discussion of Yamabe invariant (sigma constant).
result Proves new results and identifies open problems.
Study on metrics with positive scalar curvature on manifolds with singularities.
problem Understanding metrics with positive scalar curvature on manifolds with singularities.
method Proving homotopy invariance of the space of metrics with positive scalar curvature on manifolds with fibred singularities.
result Proved that the space of metrics with positive scalar curvature is homotopy invariant under certain surgeries.
We prove that every quasitoric manifold admits an invariant metric of positive scalar curvature.
New scalars measure failure of CC metrics to solve singular Yamabe problem.
problem Measuring failure of CC metrics to solve singular Yamabe problem.
method Introducing conformally invariant scalar curvature quantities along conformal infinity.
result CC boundary curvature scalars compute canonical expansion coefficients for singular Yamabe metrics.
Upper bounds on Laplacian eigenvalues on manifolds with non-negative curvature.
problem Bounding Laplacian eigenvalues on manifolds with non-negative scalar curvature.
method Investigation of invariant spectrum on compact Riemannian manifolds with large isometry groups.
result Upper bounds for eigenvalues of the invariant spectrum assuming non-negative scalar curvature.
The paper studies invariant metrics with positive scalar curvature on 3-manifolds.
problem Classifying -invariant 3-manifolds with positive scalar curvature.
method Analyzes the space of -invariant Riemannian metrics with positive scalar curvature on closed 3-manifolds.
result The space of -invariant PSC metrics is either empty or contractible.
New approach linking CR Yamabe invariant to Sasaki structures.
problem Existence of constant transversal scalar curvature Sasaki structures.
method Drawing on CR Yamabe problem ideas, establishing link between invariant, Sasaki structures, and K-stability.
result CR Yamabe invariant value determines K-semistability of Sasaki manifolds.
Study determines scalar curvature invariants for 3-spheres embedded in 4-manifolds.
problem Positive scalar curvature metrics on specific 4-manifolds.
method Relative Bauer-Furuta-type invariant on periodic-end 4-manifolds.
result Obstructions to positive scalar curvature metrics on rational homology .
Conformal invariants of manifolds of non-positive scalar curvature are studied in association with growth in volume and fundamental group.
Survey on scalar curvature stability and related questions.
problem Understanding scalar curvature stability and rigidity phenomena.
method Survey and discussion of existing tools and questions.
result Survey of known results and open questions in scalar curvature stability.
Researchers prove spaces of positive scalar curvature metrics are contractible with symmetry.
problem Contractibility of spaces of invariant positive scalar curvature metrics.
method Combining equivariant Morse theory with conformal deformations and local flexibility properties.
result Spaces of invariant positive scalar curvature metrics are contractible.
The paper proves scalar curvature lower bounds along Ricci flow on compact manifolds.
problem Preserving scalar curvature lower bounds along Ricci flow.
method Analyzing Ricci flow on compact manifolds with initial metrics having scalar curvature lower bounds.
result If initial metric has scalar curvature lower bound, it is preserved along Ricci flow.
Abstract: Characterizes spaces with positive scalar curvature.
problem Spaces with positive scalar curvature and invariant metrics.
method Cohomogeneity one manifolds and homogeneous spaces with compact Lie group actions.
result Characterization of spaces with positive scalar curvature.
We compute renormalized curvature integrals on Poincaré-Einstein manifolds.
problem Computing renormalized curvature integrals on Poincaré-Einstein manifolds.
method General procedure that connects Gauss-Bonnet-type formulas and identifies scalar conformal invariants.
result Explicit conformally invariant Gauss--Bonnet-type formulas for compact Einstein manifolds.
Study shows incompatibility of certain scalar curvatures on manifolds.
problem Incompatibility of scalar curvatures on manifolds.
method Analyzing closed manifolds with positive Yamabe invariant and positive Morse functions.
result Existence of energetically bounded solutions for related candidate functions.
Study negative scalar curvature metrics with positive boundary mean curvature.
problem Bounding conformal metrics with specific curvature properties.
method Analyzing Riemannian manifolds with boundary conditions.
result A priori boundedness of metrics in specific cases.
We extend the vanishing theorem for the Seiberg-Witten invariants of a manifold with positive scalar curvature to the case when the curvature is allowed to be negative on a set of small volume. (The precise curvature bounds are described in the paper.) The idea is to combine the method of `semigroup domination' with th…
We construct metrics of positive scalar curvature on manifolds with circle actions. One of our main results is that there exist -invariant metrics of positive scalar curvature on every -manifold which has a fixed point component of codimension 2. As a consequence we can prove that there are non-invariant metr…
We show that the higher homotopy groups of the moduli space of torus-invariant positive scalar curvature metrics on certain quasitoric manifolds are non-trivial.
New Kazdan-Warner problem for equivariant metrics on manifolds.
problem Equivariant scalar curvature functions on manifolds with group actions.
method Established equivariant analogue of Kazdan-Warner trichotomy.
result New class of totally G-positive pairs with positive constant scalar curvature.
Study eta invariant on non-compact manifolds with positive scalar curvature.
problem Proving geometric formulas and index theorems for uniformly positive scalar curvature metrics.
method Using Dirac-Schrödinger operators and relative eta invariant.
result New geometric formula for spectral flow and index formula for uniformly positive scalar curvature metrics.
We present a conformal deformation involving a fully nonlinear equation in dimension 4, starting with positive scalar curvature. Assuming a certain conformal invariant is positive, one may deform from positive scalar curvature to a stronger condition involving the Ricci tensor. We also give a new conformally invariant …
In this letter we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth order curvature invariants expressed as polynomials in , the cosmological constant. Using this invariant des…
Researchers solve the negative Yamabe case for scalar curvature prescription.
problem Prescribing scalar curvature on manifolds with negative Yamabe invariant.
method A new variational approach to the problem.
result Existence of solutions for sign-changing scalar curvature functions, but not uniqueness.
Integral of scalar curvature equals a volume ratio term on certain 3D manifolds.
problem Integral of scalar curvature on manifolds with a pole.
method Asymptotic scaling invariant integral of scalar curvature equals a term determined by asymptotic volume ratio.
result Integral of scalar curvature equals a volume ratio term.
The paper provides obstructions to positive scalar curvature for certain manifolds with group actions.
problem Obstructions to the existence of complete invariant metrics with positive scalar curvature.
method Callias-type index theorem applied to proper actions by locally compact groups.
result Obstructions to positive scalar curvature vanish for certain Lie group actions.
On a pre-quantized symplectic manifold, we show that the symplectic Futaki invariant, which is an obstruction to the existence of constant Hermitian scalar curvature almost-Kähler metrics, is actually an asymptotic invariant. This allows us to deduce a lower bound for the L^2-norm of the Hermitian scalar curvature as o…
Prove that collapsing CSC metrics can be perturbed to invariant collapsing CSC metrics.
problem Prove that collapsing constant scalar curvature metrics can be perturbed to invariant collapsing constant scalar curvature metrics.
method Prove that a sequence of constant scalar curvature metrics which is collapsing with bounded curvature to a manifold can be perturbed to a sequence of invariant collapsing constant scalar curvature metrics.
result Prove that a sequence of constant scalar curvature metrics which is collapsing with bounded curvature to a manifold can be perturbed to a sequence of invariant collapsing constant scalar curvature metrics.
We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension-2 surgery technique which removes singular strata from fixed point free -manifolds while preserving equivariant positive scalar cur…
The paper proves uniformization for specific curvature types on manifolds.
problem Uniformizing fourth order conformal curvature on Riemannian manifolds.
method Proving existence of conformal deformations for specific curvature conditions.
result Existence of conformal deformations for positive Yamabe invariant and total Q-curvature.
Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisormath.DG
We study the scalar curvature of Kähler metrics that have cone singularities along a divisor, with a particular focus on certain specific classes of such metrics that enjoy some curvature estimates. Our main result is that, on the projective completion of a pluricanonical bundle over a product of Kähler--Einstein Fano …
The Kreck-Stolz -invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being defined only under restrictive topological conditions. The aim of this paper is t…
Given a closed smooth manifold M which carries a positive scalar curvature metric, one can associate an abelian group P(M) to the space of positive scalar curvature metrics on this manifold. The group of all diffeomorphisms of the manifold naturally acts on P(M). The moduli group of positive scalar curvature metrics is…
Study on scalar curvature minimizability loss and saddle point solutions.
problem Loss of minimizability in prescribing scalar curvature.
method Variational approach, focusing on saddle point solutions.
result Existence of saddle point solutions despite minimizability loss.
New invariant extends curvature estimates to noncompact manifolds.
problem Estimating scalar curvature in noncompact manifolds.
method Introducing vertical \(\widehat{A}\)-cowaist and using deformed Dirac operators.
result Sharp inequality relating scalar curvature, spectrum, and new invariant.
Let G be a discrete group, and let M be a closed spin manifold of dimension m>3 with pi_1(M)=G. We assume that M admits a Riemannian metric of positive scalar curvature. We discuss how to use the L2-rho invariant and the delocalized eta invariant associated to the Dirac operator on M in order to get information about t…
Derives scalar curvature formula in generalized Kähler geometry.
problem Formalizes scalar curvature in generalized Kähler geometry.
method Uses moment map and action of generalized Hamiltonian automorphisms.
result Derives explicit formula for Goto's scalar curvature.
In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for computing sectional curvatures of these metrics and show that all these spaces have …
We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume G-invariant metrics minimizing the total scalar curvature functional in their …
Study on Kähler metrics on ruled surfaces, proving existence and non-existence.
problem Existence and non-existence of Kähler metrics on minimal ruled surfaces.
method Analysis of twisted and coupled constant scalar curvature Kähler metrics.
result Bound for Chen-Cheng invariant on ruled surfaces.