Let X be a smooth projective curve of genus g ≥ 2 defined over a field of characteristic two. We give examples of stable orthogonal bundles with unstable underlying vector bundles and use them to give counterexamples to Behrend’s conjecture on the canonical reduction of principal G-bundles for G = SO(n) with n ≥ 7. Let X be a smooth projective curve of genus g ≥ 2 and let G be a connected reduc...

In this note, we examine the relationship between the twisting of a vector bundle ξ over a manifold M and the action of the holonomy group of a Riemannian connection on ξ. For example, if there is a holonomy group which does not act transitively on each fiber of the corresponding unit sphere bundle, then for any f : Sn → M , the pullback f∗ξ of ξ admits a nowhere-zero cross section. These facts...

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on compact manifold, by computing its base-like cohomology. As an application, we prove that if is non-unimodular then either ambient closure leaves or total space associated principal bundle fiber over S 1 .

Natural convection heat transfer from a tube bundle in the indirect water bath heaters is investigated. A computer-code is used for the solution of the governing equations of mass, momentum and energy transfer based on the SIMPLE-C algorithm. Simulations are carried out for the gas pressure station heater of Kermanshah city with various tube bundle arrangements. In order to validate the numeric...

Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on a configuration manifold Q, considers its natural cotangent lift to T ∗Q and then one seeks realizations of the corresponding symplectic or Poisson reduced space. We further develop this theory by ...

Let G ~ Sp (n, R) be the symplectic group (n~i) and G 6 be the same group with the discrete topology. The present paper is devoted to the study of the element u of the group H ~ (G~; Z), which is determined up to sign in any of the following (equivalent) ways: a) u is the image under the canonical homomorphism H 2 (BG; Z)-~ H 2 (BG~: Z) of the generator of the group H 2 (BG; Z)~ Z; b# u is the ...

Let R ∗ = R2k+1 \ {~0} (k ≥ 1) and π: R ∗ → S2k be the map sending ~r ∈ R ∗ to ~r |~r| ∈ S 2k . Denote by P → R ∗ the pullback by π of the canonical principal SO(2k)-bundle SO(2k + 1) → S2k . Let E] → R ∗ be the associated co-adjoint bundle and E] → T ∗R ∗ be the pullback bundle under projection map T ∗R ∗ → R ∗ . The canonical connection on SO(2k + 1) → S2k turns E] into a Poisson manifold. Th...

Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on a connguration manifold Q, considers its natural cotangent lift to T Q and then one seeks realizations of the corresponding symplectic or Poisson reduced space. We further develop this theory by ex...