A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Spinorial approach characterizes submanifolds in product spaces of constant curvature.
In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Lie groups equipped with left invariant metrics. As applications, we get a spinorial proof of the Fundamental Theorem for submanifolds into Lie groups, we recover previously known representations of submanifolds in $\…
Paper proves a spinorial version of Aubin's estimate for the Yamabe problem.
In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of so called generalized Killing spinors. We then discuss several applications, among them a new and concise proof of the fundamental theorem of submanifold theory. We …
Paper defines a new functional for spinors on Euclidean manifolds.
Compact proof for Brown-York mass positivity and rigidity in flat and spherical spaces.
Paper proves existence of minimum energy solutions in 5D contact spin manifolds.
Revises Schwarzschild manifold rigidity proof for spin manifolds.
New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of Atiyah-Patodi-Singer type. Spinorial techniques are used to give simple proofs …
We describe the different classes of structures in terms of spinorial equations. We relate them to the spinorial description of structures in some geometrical situations. Our approach enables us to analyze invariant structures on quasi abelian Lie algebras.
We prove that an isometric immersion of a simply connected Riemannian surface M in four-dimensional Minkowski space, with given normal bundle E and given mean curvature vector H \in Γ(E), is equivalent to a normalized spinor field \varphi \in Γ(ΣE \otimes ΣM) solution of a Dirac equation D\varphi=H\cdot\varphi on the s…
In this paper we give a geometrically invariant spinorial representation of surfaces in four-dimensional space forms. In the Euclidean space, we obtain a representation formula which generalizes the Weierstrass representation formula of minimal surfaces. We also obtain as particular cases the spinorial characterization…
Let $(M,g,\si)$ be a compact Riemannian spin manifold of dimension . For any metric conformal to , we denote by the first positive eigenvalue of the Dirac operator on $(M,\tilde g,\si)$. We show that $$\inf_{\tilde{g} \in [g]} \tildeλ\Vol(M,\tilde g)^{1/n} \leq (n/2) \Vol(S^n)^{1/n}.$$ T…
Researchers found a spinorial representation for surfaces in 3D Lorentzian spaces.
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin structure carrying a partially pure spinor field. We study various integrability conditions of the alm…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, …
Study on solutions to spinorial Yamabe equation on manifolds with boundary.
We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.
This is a companion paper to arXiv:1207.3529 where we introduced the spinorial energy functional and studied its main properties in dimensions equal or greater than three. In this article we focus on the surface case. A salient feature here is the scale invariance of the functional which leads to a plenitude of critica…
This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: …
Using spinorial techniques, we prove, for a class of pseudo-hyperbolic ambient manifolds, a Heintze-Karcher type inequality. We then use this inequality to show an Alexandrov type theorem in such spaces.
Study spinorial Yamabe problem on product manifolds, proving spike layer solutions.
Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists \cite{onish1} and we treat in detail the only new series of inclusions providing the spinorial structur…
Initial data with zero mass must be in pp-wave spacetimes.
We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in to other Lorentzian space forms. We also characterize immersions of Riemannia…
An explicit lower bound for the mass of an asymptotically flat Riemannian 3-manifold is given in terms of linear growth harmonic functions and scalar curvature. As a consequence, a new proof of the positive mass theorem is achieved in dimension three. The proof has parallels with both the Schoen-Yau minimal hypersurfac…
New mass definition for negative cosmological constant spacetimes.
The paper extends Descartes' circle theorem to n-flower configurations using hyperbolic geometry.
The paper finds bounds for a spinorial equation and applies it to a Bär-Hijazi-Lott invariant.
Refines spinorial Sobolev inequality on sphere, proving stability and new properties of Killing spinors.
Spinorially constructs Sasakian and 3-Sasakian structures in arbitrary dimensions.
This paper studies non-compactness in spinorial Yamabe-type problems on manifolds.
The Witten spinorial argument has been adapted in several works over the years to prove positivity of mass in the asymptotically AdS and asymptotically hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar curvature rigidity result and a positive mass theorem for asymptotically hyperbolic manifol…
On a compact surface endowed with any $\Spinc$ structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a Bär-type inequality for the eigenvalues of the Dirac operator is given. The round sphere with its canonical $\Spinc$ structure satisfies the …
We give a spinorial representation of a submanifold of any dimension and co-dimension in a symmetric space where is a complex semi-simple Lie group and is a compact real form of This in particular includes and extends the previously known spinorial representation of a surfa…
Defines a spinorial quasilocal mass for compact manifolds.
Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the -sphere, . Via variational methods and the spinorial Weierstraß representation, we study the problem of prescribing mean curvature for the imme…
We consider a spinorial Yamabe-type problem on open manifolds of bounded geometry. The aim is to study the existence of solutions to the associated Euler-Lagrange-equation. We show that under suitable assumptions such a solution exists. As an application, we prove that existence of a solution implies the conformal Hija…
New spinorial field equation reveals geometric properties of Sasaki manifolds.
The concept of pure spinor is generalized, giving rise to the notion of pure subspaces, spinorial subspaces associated to isotropic vector subspaces of non-maximal dimension. Several algebraic identities concerning the pure subspaces are proved here, as well as some differential results. Furthermore, the freedom in the…
Study on spinor field equation on spheres, focusing on blow-up analysis.
We present a uniform description of -structures in dimension as well as -structures in dimension in terms of a characterising spinor and the spinorial field equations it satisfies. We apply the results to hypersurface theory to obtain new embedding theorems, and give a general recipe for bu…
In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants are characterized through Yamabe-type equations on products of spheres with rescal…
Upper bound found for systolic geometry on manifolds with positive scalar curvature.
We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This generalizes results by T. Friedrich for and B. Morel for $\Ss^3$ and $\HH^3$…
Unified framework for Riemannian, Kahler, and hyper-Kahler geometries in 4D.
We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that …
Proves principles and estimates for initial data sets in Einstein equations.