‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

The aim of this paper is to extend the notion all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed manifold, pseudo manifold and many more name it comprehensive quasi Einstein C(QE)$_{n}$. We investigate some geometric physical properties C(QE)$_{n}$ under certain conditions. study conformal conharmonic mappings between manifolds. Then we examine with harmonic Weyl tensor. ...

for any tangent vectors X,Y to M . If the almost complex structure J is integrable we obtain a Kähler structure. Many efforts have been done in the direction of finding curvature conditions on the metric which insure the integrability of the almost complex structure. A famous conjecture of Goldberg [26] states that a compact almost Kähler, Einstein manifold is in fact Kähler. Important progress...

Let ( $${\cal M}$$ , g0) be a compact Riemannian manifold-with-boundary. We present new proof of the classical Gaffney inequality for differential forms in boundary value spaces over via variational approach à la Kozono-Yanagisawa [Lr-variational vector fields and Helmholtz-Weyl decomposition bounded domains, Indiana Univ. Math. J. 58 (2009), 1853–1920], combined with global computations based ...

In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete manifold with fourth-order divergence-free Weyl tensor zero radial curvature is locally warped product $(n-1)$-dimensional Einstein fibers, provided the potential function proper. As consequence, result about nonexistence of mult...

Let R be a root system. Let W be the corresponding affine Weyl group, and let Ŵ be an extended affine Weyl group. Let H (respectively Ĥ) be the corresponding Hecke algebras. George Lusztig defined an asymptotic version of the Hecke algebra, the ring J , see [10]. By definition the ring J is a direct sum J = ⊕ c Jc where summation is over the set of two-sided cells in the affine Weyl group. Furt...

In the literatures, several types of thick smooth brane configurations in a pure geometric Weyl integrable 5-dimensional space time have been presented. The Weyl geometry is a non-Riemannian modification of 5-dimensional Kaluza–Klein (KK) theory. All these thick brane solutions preserve 4-dimensional Poincaré invariance, and some of them break Z2–symmetry along the extra dimension. In this pape...

We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resulting system of Euler–Lagrange equations. In the first part of the paper we lo...

We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space common equilibrium points defined by its leading term. On this space, we construct local which forms an exact Poisson pencil, defines algebraic classical W-algebra, admits dispersionless limit, term Frobenius manifold. This leads to uniform construction manifo...