Modeling and understanding complex non-manifold shapes is a key issue in shape analysis and retrieval. The topological structure of a non-manifold shape can be analyzed through its decomposition into a collection of components with a simpler topology. Here, we consider a representation for arbitrary shapes, that we call ManifoldConnected Decomposition (MC-decomposition), which is based on a uni...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

We consider 6-dimensional nearly Kähler manifolds M and prove that any totally geodesic hypersurface N of M is a Sasaki-Einstein manifold, and so it has a hypo structure in the sense of [8]. We show that such a hypo structure defines a nearly Kähler structure on N × R, and a compact nearly Kähler structure with conical singularities on N 5 × S 1 when N is compact. Moreover, an extension of the ...

In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...

We consider the Hermitian-Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle E over an almost complex manifold X which is the twistor space of an oriented Riemannian manifold M. Each solution of the HYM equations on such X defines a pseudoholomorphic structure on the bundle E . It is shown that the pull-back to X of any anti-selfdual gauge field on M is a solution of the...

In this paper, we construct metallic Kähler and nearly structures on Riemannian manifolds. For such manifolds with these structures, study curvature properties. Also, describe linear connections the manifold which preserve associated fundamental [Formula: see text]-form satisfy some additional conditions present results concerning them.

We review basic facts on the structure of nearly K\"ahler manifolds, focussing in particular six-dimensional case. A self-contained proof that six-manifolds are Einstein is given by combining different known results. finally rephrase definition six-manifold terms a pair partial differential equations.

We find Weitzenb\"ock formula for the Fueter-Dirac operator which controls infinitesimal deformations of an associative submanifold in a $7$--manifold with $G_2$--structure. establish vanishing theorem to conclude rigidity under some positivity assumptions on curvature, are particularly mild nearly parallel case. As applications, we give different proof one Lotay's associatives round $7$-sphere...