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.
Odd-dimensional Riemannian manifolds admit pure spin-c Killing spinors if and only if they are α-Sasakian.
In this paper, we extend the study of generalized Killing spinors on Riemannian Spin manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spin Killing spinors or imaginary generalized Spin Killing spinors, providing that the dimension of t…
New spinor fields reveal local or global geometric properties of manifolds.
On manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and po…
Develops complex spinorial forms for all dimensions and signatures, proving Brinkmann waves in supergravity.
We extend to the eigenvalues of the hypersurface Spin Dirac operator well known lower and upper bounds. Examples of limiting cases are then given. Futhermore, we prove a correspondence between the existence of a Spin Killing spinor on homogeneous 3-dimensional manifolds with 4-dimensional is…
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
The paper characterizes new invariant spin spinors on projective spaces.
Classifies manifolds with specific spinors and constructs parallel spinors.
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian …
In this paper we use the G-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic 4-manifold that admits harmonic spinors. We also explicitly describe the Spinor bundle of a spin hyperbolic 2- or 4-manifold and show how to calculated the subtl…
The article studies spinor and tensor fields on curved spaces, deriving formulas and spectra.
Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.
Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.
In this review, basic definitions of spin geometry are given and some of its applications to supersymmetry, supergravity and condensed matter physics are summarized. Clifford algebras and spinors are defined and the first-order differential operators on spinors which lead to the definitions of twistor and Killing spino…
Researchers compute the ν-invariant for specific G2-structures on nilmanifolds.
Extends spinor-horosphere correspondence to higher dimensions and new spinor types.
Calculates spinor heat flow using Gaussian-Grassmann integrals.
A closed spin Kähler manifold of positive scalar curvature with smallest possible first eigenvalue of the Dirac operator is characterized by holomorphic spinors. It is shown that on any spin Kähler-Einstein manifold each holomorphic spinor is a finite sum of eigenspinors of the square of the Dirac operator. Vanishing t…
Study uncoupled solutions to Dirac-Yang-Mills equations on spin manifolds.
Newly characterizes the Standard Model gauge group using spinors and geometry.
On a Kähler spin manifold Kählerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the Kähler structure, called Kählerian twistor (Penrose) operator. We study Kählerian twistor spinors a…
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular structures. The limiting case is characterized by the existence of Kählerian Killing spinors in a certain subbundle of…
The paper proves stability for Einstein metrics with special twisted spinors.
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin case the result of O. Kowalski stating that, every totally umbilical hypersurface of an Einstein manif…
We study conformal -subgeometry of submanifolds in a semi-Riemannian -manifold, focusing on conformal -manifolds and their Poincaré-Einstein metrics . Our approach is based on the spectral theory of Dirac operator in the ambient -manifold, and associated spinor valued meromorp…
A beautiful solution to the problem of isometric immersions in using spinors was found by Bayard, Lawn and Roth. However to use spinors one must assume that the manifold carries a $\mbox{Spin}$-structure and, especially for complex manifolds where is more natural to consider $\mbox{Spin}^{\mathbb{C}}$-st…
The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) …
New criterion for Ricci-flat manifolds with non-vanishing Rosenberg index.
We describe, by their holonomy groups, all complete simply connected irreducible non-locally symmetric pseudo-Riemannian SpinC manifolds which admit parallel spinors. So we generalize the Riemannian SpinC case and the pseudo-Riemannian Spin one.
Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of this composite spinor bundle are canonically defined.
Simply connected 3-dimensional homogeneous manifolds , with 4-dimensional isometry group, have a canonical Spin structure carrying parallel or Killing spinors. The restriction to any hypersurface of these parallel or Killing spinors allows to characterize isometric immersions of surfaces into . As…
We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin manifolds by the existence of a Spin structure carrying a strictly partially pure spinor field. Furthermore, we study the geometry of Riemannian Spin manifolds carrying a strictly partially pure spi…
The complex projective space of complex dimension has a Spin structure carrying Kählerian Killing spinors. The restriction of one of these Kählerian Killing spinors to a surface characterizes the isometric immersion of into if the immersion is either Lagrangian or com…
We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of , explicit representations…
Classifies invariant spinors on nine sphere types.
Geometric correspondence between spinors and horospheres in hyperbolic space.
We derive various pinching results for small Dirac eigenvalues using the classification of and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for manifolds which involves a general study on convergence of Riemannian manifolds with a pr…
It is well known that spinors on oriented Riemannian manifolds cannot be defined as sections of a vector bundle associated with the frame bundle. For this reason spin and spin^c structures are often introduced. In this paper we prove that spin^c structures have a universal property among all other structures that enabl…
Study on harmonic spinors on specific Lie groups.
We show that on every Spin(7) manifold there always exists a unique linear connection with totally skew-symmetric torsion preserving a nontrivial spinor and the Spin(7) structure. We express its torsion and the Riemannian scalar curvature in terms of the fundamental 4-form. We present an explicit formula for the Rieman…
The paper characterizes spin initial data sets saturating the BPS bound in asymptotically AdS spacetimes.
The paper extends Strichartz's conjecture to spinor bundles over real hyperbolic spaces.
In this paper we discuss the twistor equation in Lorentzian spin geometry. In particular, we explain the local conformal structure of Lorentzian manifolds, which admit twistor spinors inducing lightlike Dirac currents. Furthermore, we derive all local geometries with singularity free twistor spinors that occur up to di…
New spinor types found on certain manifolds.
The paper proves vanishing theorems for harmonic forms and spinors on stable minimal hypersurfaces.
We describe and to some extent characterize a new family of Kähler spin manifolds admitting non-trivial imaginary Kählerian Killing spinors.
Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains conformal spin structures. The resulting conformal spin geometries are then character…