Related papers: On balanced Hermitian threefolds with parallel Bis…

We compare the notions of metric-compatibility and torsion of a connection in the frameworks of Beggs-Majid and Mesland-Rennie. It follows that for $\ast$-preserving connections, compatibility with a real metric in the sense of Beggs-Majid…

We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.

The object of study in the present dissertation are some topics in differential geometry of smooth manifolds with additional tensor structures and metrics of Norden type. There are considered four cases depending on the dimension of the…

In this paper we provide examples of hypercomplex manifolds which do not carry HKT structure. We also prove that the existence of HKT structure is not stable under small deformations. Similarly we provide examples of compact complex…

The geometry arising from Michelson & Strominger's study of N=4B supersymmetric quantum mechanics with superconformal D(2,1;alpha)-symmetry is a hyperKaehler manifold with torsion (HKT) together with a special homothety. It is shown that…

In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.

We consider non-Kaehler compact complex manifolds which are homogeneous under the action of a compact Lie group of biholomorphisms and we investigate the existence of special (invariant) Hermitian metrics on these spaces. We focus on a…

In this paper we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces.In particular, using the moving frame method, we prove that $\mathbb{CP}^3$ is the only twistor space whose Bochner tensor is…

The twisted torsion of a 3-manifold is well-known to be zero whenever the corresponding twisted Alexander module is non-torsion. Under mild extra assumptions we introduce a new twisted torsion invariant which is always non-zero. We show how…

We consider a closed odd-dimensional oriented manifold $M$ together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a natural…

A discussion of torsion of Riemannian G-structures leads to a survey of contributions of Alfred Gray and others on almost Hermitian manifolds, G_2-manifolds, curvature identities, volume expansions, plotting geodesics, and the geometry of…

For any ring $R$, we investigate balanced pairs of classes of modules and their relations to cotorsion triples. We characterize the case when a balanced pair generates a tilting cotorsion pair, and dually, when it cogenerates a cotilting…

We study tautness properties of a Riemannian foliation by investigating a symmetric 2-tensor associated with the mean curvature of the foliation. As a consequence, we prove a tautness condition for Riemannian foliations on compact manifolds…

We describe a family of 3d topological B-models whose target spaces are Hilbert schemes of points in $\mathbb{C}^2$. The interfaces separating theories with different numbers of points correspond to braid strands. The Hilbert space of the…

The quantum geometric tensor (QGT) characterizes the complete geometric properties of quantum states, with the symmetric part being the quantum metric, and the antisymmetric part being the Berry curvature. We propose a generic Hamiltonian…

Under some suitable assumptions Riemannian manifolds $(M, g, H)$ that admit a connection $\hat\nabla$ with torsion a 3-form $H$, which is both closed $d H=0$ and $\hat\nabla$-covariantly constant, are locally isometric to a product $N\times…

The well-known fact that $S^1$, $S^3$ and $S^7$ are parallelizable manifolds admitting flat connections is revisited. The role of torsion in the construction of those flat connections is made explicit, and the possibilities allowed by…

We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new…

A natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric is constructed. The class of these manifolds, where the considered connection exists, is determined. Some curvature properties for this…

We study quaternionic Bott-Chern cohomology on compact hypercomplex manifolds and adapt some results from complex geometry to the quaternionic setting. For instance, we prove a criterion for the existence of HKT metrics on compact…