Related papers: Riemannian manifolds with structure group PSU(3)

We consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic…

We develop an invariant approach to $SU(2)$--structures on spin $5$--manifolds. We characterize (via spinor approach) the subspaces in the spinor bundle which induce the same group isomorphic to $SU(2)$. Moreover, we show how to induce…

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 deformations of geometric structures on some LVM manifolds of complex dimension $3$. More precisely, we study resonant structures, a particular type of $(G,X)$-structures, via the Ehresmann-Thurston principle, and their link with…

The group SU(3) is parameterized in terms of generalized ``Euler angles''. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is…

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds…

We consider a 4-dimensional Riemannian manifold M endowed with a right skew-circulant tensor structure S, which is an isometry with respect to the metric g and the fourth power of S is minus identity. We determine a class of manifolds (M,…

One way of producing explicit Riemannian 6-manifolds with holonomy SU(3) is by integrating a flow of SU(2)-structures on a 5-manifold, called the hypo evolution flow. In this paper we classify invariant hypo SU(2)-structures on nilpotent…

We study and in some cases classify highly connected manifolds which admit a Riemannian metric with positive $p$-curvature. The $p$-curvature was defined and studied by the second author. It turns out that positivity of $p$-curvature could…

We consider a 3-dimensional Riemannian manifold with additional structure q. We find a condition that the affine structure q is parallel with respect to the Riamannian connection.We prove the sectional curvatures of three 2-sections formed…

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…

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…

The unit sphere $\mathbb S^3$ can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding…

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

The invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is…

Taking [math/0606786] as an inspiration, we study the intrinsic torsion of a SU(2) structure manifold in six dimensions to give a formula for the Ricci scalar in terms of torsion classes. The derivation is founded on the SU(3) result coming…

The holonomy of the Bismut connection on Vaisman manifolds is studied. We prove that if $M^{2n}$ is endowed with a Vaisman structure, then the holonomy group of the Bismut connection is contained in U$(n-1)$. We compute explicitly this…

Concepts and techniques from the theory of G-structures of higher order are applied to the study of certain structures (volume forms, conformal structures, linear connections and projective structures) defined on a pseudo-Riemanniann…

We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the…

The primary aim of this thesis is to investigate metrics which are induced by a differential form and arise as a critical point of Hitchin's variational principle. Firstly, we investigate metrics associated with the structure group PSU(3)…