Related papers: Clifford structures on Riemannian manifolds

This is a survey of old and new results on the problem when a compatible almost complex structure on a Riemannian manifold is a harmonic section or a harmonic map from the manifold into its twistor space. In this context, a special…

Using vertical and complete lifts, any left invariant Riemannian metric on a Lie group induces a left invariant Riemannian metric on the tangent Lie group. In the present article we study the Riemannian geometry of tangent bundle of two…

We develop a unifed theory to study geometry of manifolds with different holonomy groups. They are classified by (1) real, complex, quaternion or octonion number they are defined over and (2) being special or not. Specialty is an…

In this paper we study collapsing sequences M_{i}-> X of Riemannian manifolds with curvature bounded or bounded away from a controlled subset. We introduce a structure over X which in an appropriate sense is dual to the N-structure of…

We prove that any $4$-dimensional almost-K\"ahler Lie algebra of constant Hermitian holomorphic sectional curvature with respect to the canonical Hermitian connection is K\"ahler.

We introduce the notion of a rank-3 generalized Clifford manifold, defined by a triple of generalized complex structures satisfying Clifford-type relations. We show that every such structure canonically induces a generalized hypercomplex…

We propose a generalization of two classes of Lie-Hamilton systems on the Euclidean plane to two-dimensional curved spaces, leading to novel Lie-Hamilton systems on Riemannian spaces (flat $2$-torus, product of hyperbolic lines, sphere and…

We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of…

Let L\subset V=\bR^{k,l} be a maximally isotropic subspace. It is shown that any simply connected Lie group with a bi-invariant flat pseudo-Riemannian metric of signature (k,l) is 2-step nilpotent and is defined by an element \eta \in…

We construct the explicit form of three almost complex structures that a Riemannian manifold with self-dual curvature admits and show that their Nijenhuis tensors vanish so that they are integrable. This proves that gravitational instantons…

We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop space. We show that this bundle is in general non-trivial,…

Almost para-quaternionic structures on smooth manifolds of dimension $2n$ are equivalent to almost Grassmannian structures of type $(2,n)$. We remind the equivalence and exhibit some interrelations between subjects that were previously…

Let $X$ be a smooth projective scheme and $E$ a vector bundle on $X$. For a relative hypersurface $Y_f \subset \mathbb{P}(E)$ of degree $d$ defined by a global section $f$, we establish a functorial equivalence between the category of…

On a sub-Riemannian manifold, a connection with skew-symmetric torsion is defined as the unique connection from the class of $N$-connections that has this property. Two cases are considered separately: sub-Riemannian structure of even rank,…

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi-Clifford curvature tensors using a…

We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of…

Since the work of Henri Cartan finite dimensional Riemannian symmetric spaces are an important subject of mathematical interest. They are related in a natural way to semisimple Lie groups. In this work we introduce and study their infinite…

We find geometric conditions on a four-dimensional Hermitian manifold endowed with a metric connection with totally skew-symmetric torsion under which the complex structure is a harmonic map from the manifold into its twistor space…

Using quaternionic Feix--Kaledin construction we provide a local classification of quaternion-K\"ahler metrics with a rotating $S^1$-symmetry with the fixed point set submanifold $S$ of maximal possible dimension. For any K\"ahler manifold…