On an almost complex manifold, a quasi-Kähler metric, with canonical connection in the c-projective class of given minimal connection, is equivalent to nondegenerate solution c-projectively invariant metrizability equation. For this overdetermined equation, replacing maximal rank condition on solutions nondegeneracy prolonged system yields strictly wider non-vanishing (generalized) scalar curva...

The study of magnetic curves, seen as solutions Lorentz equation, has been done mainly in 3-dimensional case, motivated by theoretical physics. Then it was extended higher dimensions, for instance K?hlerian or Sasakian frame. This paper deals the first time literature with Frenet curves dimensional paracontact context. Several classifications are provided here different types on para-Sasakian m...

We characterize the Einstein metrics in such broad classes of as almost $$\eta $$ -Ricci solitons and on Kenmotsu manifolds, generalize some known results. First, we prove that a metric an soliton is if either it -Einstein or potential vector field V infinitesimal contact transformation collinear to Reeb field. Further, manifold admits gradient with leaving scalar curvature invariant, then mani...

The object of this offering article is to introduce the notion *- Miao-Tam critical equation on almost contact metric manifolds and it studied Kenmotsu with some nullity condition. It proved that if a (2n + 1)-dimensional (k, µ)!-almost manifold (M, g) satisfies *-Miao-Tam equation, then *-Ricci flat locally isometric product space. Finally, result verified by an example.

On an almost Hermitian manifold, there are two scalar curvatures associated with a canonical connection. In this paper, explicit formulas on these obtained in terms of the Riemannian curvature, norms components covariant derivative fundamental 2-form respect to Levi-Civita connection, and codifferential Lee form. Then we use them get characterization results Kähler metric, balanced locally conf...

We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as sections twistor for a given metric. For connected six-manifold with vanishing first Betti number, we express quotient seven-sphere bundle over manifold by circle action, and then use this description to compute rational homotopy theoretic minimal model components that satisfy certain Chern numbe...

In this paper, we construct a framed f -structure on the slit tangent space of a Rizza manifold. This induces on the indicatrix bundle an almost contact metric. We find the conditions under which this structure reduces to a contact or to a Sasakian structure. Finally we study these structures on Kählerian Finsler manifolds. M.S.C. 2010: 53B40, 53C60, 32Q60, 53C15.

We show that any non-Kähler, almost Kähler 4-manifold for which both the Ricci and the Weyl curvatures have the same algebraic symmetries as they have for a Kähler metric is locally isometric to the (only) proper 3-symmetric four-dimensional space. Mathematics Subject Classifications (2000): Primary 53B20, 53C25.

We study ergodic random Schrödinger operators on a covering manifold, where the randomness enters both via the potential and the metric. We prove measurability of the random operators, almost sure constancy of their spectral properties, the existence of a selfaveraging integrated density of states and a Šubin type trace formula.

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M, J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M, J).