The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only i...

In this article we show that every smooth closed oriented fourmanifold admits a decomposition into two submanifolds along common boundary. Each of these submanifolds is a complex manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-manifold is a Stein domain in the the complement of a certain contractible 2-complex.

The wave type field equation θ = λθ, where θ is a coframe field on a space-time, was recently proposed to describe the gravity field. This equation has a unique static, spherical-symmetric, asymptotically-flat solution, which leads to the viable Yilmaz-Rosen metric. We show that the wave type field equation is satisfied by the pseudo-conformal frame if the conformal factor is determined by a sc...

In this paper, we classify almost cosymplectic 3-manifolds with pseudo-parallel characteristic Jacobi operator. The only simply connected and complete non-cosymplectic 3-manifold pseudo parallel operator is the Minkowski motion group.

In terms of synthetic differential geometry, we give a variational characterization of the connection (parallelism) associated to a pseudo-Riemannian metric on a manifold.

In this paper, we study the theory of geodesics with respect to the TanakaWebster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some HopfRinow type, Cartan-Hadamard type and Bonnet-Myers type results are established.

Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary pseudo-spline subdivision schemes. We show that their masks have positive Fourier transform, makin...

Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. The aim of this paper is to investigate the internal states and the state-morphisms on pseudo equality algebras. We define and study new classes of pseudo equality algebras, such as com...

The number of functionally independent scalar invariants of arbitrary order of a generic pseudo–Riemannian metric on an n–dimensional manifold is determined.