相关论文: Spin structures and spectra of $Z_2^k$-manifolds

For each integer $d$ at least two, we construct non-spin closed oriented flat manifolds with holonomy group $\mathbb Z_2^d$ and with the property that all of their finite proper covers have a spin structure. Moreover, all such covers have…

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…

We give a necessary and suffcient condition for almost-flat manifolds with cyclic holonomy to admit a Spin structure. Using this condition we find all 4-dimensional orientable almost- flat manifolds with cyclic holonomy that do not admit a…

It is shown that every bundle $\varSigma\to M$ of complex spinor modules over the Clifford bundle $\Cl(g)$ of a Riemannian space $(M,g)$ with local model $(V,h)$ is associated with an lpin ("Lipschitz") structure on $M$, this being a…

Let $$M_{n}\stackrel{\mathbb R P^1}\to M_{n-1}\stackrel{\mathbb R P^1}\to\ldots\stackrel{\mathbb R P^1}\to M_{1}\stackrel{\mathbb R P^1}\to M_0 = \{ \bullet\} $$ be a sequence of real projective bundles such that $M_i\to M_{i-1}$,…

We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unitary spinor. Such structures are related to SU(2) (dim=4,5), SU(3) (dim=6) and G_2 (dim=7)…

We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H, g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also…

We use classical obstruction theory \`{a} la Eilenberg-Steenrod to obtain a homotopy classification of $\mathrm{Spin}(7)$-structures on compact $8$-manifolds with abelian fundamental group. As an application, we show that a compact,…

We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors.

This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in…

We find all m-spin structures on Klein surfaces of genus larger than one. An m-spin structure on a Riemann surface P is a complex line bundle on P whose m-th tensor power is the cotangent bundle of P. A Klein surface can be described by a…

Let M be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa\'{n}ski…

We describe, by their holonomy groups, all simply connected irreducible non-locally symmetric pseudo-Riemannian SpinC manifolds which admit parallel spinors. So we generalise the Riemannian case and the pseudo-Riemannian one.

The group Spin(7) belongs to the list of possible holonomy of an eight-dimensional Riemannian manifold. The weaker notion of Spin(7)-structures plays for manifolds with holonomy Spin(7), the analogue of almost Hermitian for K{\"a}hler…

We present an algorithmic approach to the problem of existence of spin structures on flat manifolds. We apply our method in the cases of flat manifolds of dimensions 5 and 6.

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…

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…

It is well-known that the spectrum of a $\text{spin}^{\mathbb{C}}$ Dirac operator on a closed Riemannian $\text{spin}^{\mathbb{C}}$ manifold $M^{2k}$ of dimension $2k$ for $k \in \mathbb{N}$ is symmetric. In this article, we prove that over…

It is well-known that any covering space of a Riemannian manifold has the natural structure of a Riemannian manifold. This article contains a noncommutative generalization of this fact. Since any Riemannian manifold with a Spin-structure…

This paper investigates the geometric structures and properties of 8-dimensional manifolds with Spin(7)-holonomy. We focus on the characterization and implications of 4-planes within these manifolds, which are endowed with an almost…