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...

the present article serves the purpose of pursuing geometrization of heat flow on volumetrically isothermal manifold by means of rf approach. in this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of riemannian manifold and fundamental properties of thermodynamic systems. by making use of the notions of various curva...

Stability and chaoticity in conservative Hamiltonian systems are analyzed using an indicator based on a generalization of the virtual work principle (VWP) for Riemannian manifolds. The geometrodynamic formalism obtained this way is applied to define mechanical manifold Jacobi metric, where system trajectories geodesics. VWP static equilibrium Euclidean spaces generalized through geodesic equati...

The notion of convergent star product is generally understood as the data of a one parameter family {Et}t∈I ⊂ C∞(M) of function algebras on a Poisson manifold (M, { , }). On each of them one is given an associative algebra structure ⋆t which respect to which the function space Et is closed. The family of products {⋆t} should moreover define in some sense a deformation of the commutative pointwi...

Abstract. A curvature-type tensor invariant called quaternionic contact (qc) conformal curvature is defined on a qc manifolds in terms of the curvature and torsion of the Biquard connection. The discovered tensor is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser invariant in CR geometry. It is shown that a qc manifold is locally qc conformal to the standar...

Let W be a crystallographic Weyl group, and let TW be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W , and its weight lattice. The real locus TW (R) is a smooth, connected, compact manifold with a W -action. We give a formula for the Euler characteristic of TW (R) as a generalised character of W . In type An−1 for n odd, one obtains a gen...

of the Dissertation Self-Dual Metrics on 4-Manifolds by Mustafa Kalafat Doctor of Philosophy in Mathematics Stony Brook University 2007 Under a vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-Manifolds is again self-dual. Here we prove that the same result can be extended over to the positive scalar curvature case. Secondly we give an exa...

Conjecture. Let G be a compact Lie group which acts isometrically on a complete Riemannian manifold M , such that this action admits a section: There exists a closed submanifold Σ in M which meets each orbit orthogonally. Then the space Ωhor(M) of all differential forms on M which are invariant under the G-action and are horizontal in the sense that they kill each vector which is tangent to an ...

Let M be a compact locally conformal hyperkähler manifold. We prove a version of Kodaira-Nakano vanishing theorem for M . This is used to show that M admits no holomorphic differential forms, and the cohomology of the structure sheaf H(OM ) vanishes for i > 1. We also prove that the first Betti number of M is 1. This leads to a structure theorem for locally conformally hyperkähler manifolds, de...