The symmetric algebra S(g) over a Lie algebra g has the structure of a Poisson algebra. Assume g is complex semisimple. Then results of Fomenko–Mischenko (translation of invariants) and A. Tarasev construct a polynomial subalgebra H = C[q1, . . . , qb] of S(g) which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of g. Let G be the adjoint group of g and let l = ...

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...

Let (M, g) be a closed Riemannian manifold (m ≥ 2) of positive scalar curvature and (N, h) any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second N−Yamabe constant of (M × N, g + th) as t goes to +∞. We obtain that limt→+∞ Y (M ×N, [g+ th]) = 2 2 m+n Y (M ×R, [g+ ge]). If n ≥ 2, we show the existence of nodal solutions of the Yamabe equation on (M × ...

We study the de Rham 1-cohomology H 1 DR (M, G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principal bundle M × G by the so-called gauge equivalence. We consider the case when M is a compact Kähler manifold and G is a solvable complex linear algebraic group of a special class which contains the Borel sub...

The object of the upcoming article is to characterize paracontact metric manifolds conceding $m$-quasi Einstein metric. First we establish that if $g$ in a $K$-paracontact manifold metric, then constant scalar curvature. Furthermore, classify $(k,\mu)$-paracontact whose Finally, construct non-trivial example such manifold.

In this paper we consider pseudo projectively flat Riemannian manifold whose Ricci tensor S satisfies the condition S(X,Y ) = rT (X)T (Y ), where r is the scalar curvature, T is a non-zero 1-form defined by g(X, ξ) = T (X), ξ is a unit vector field and prove that the manifold is of pseudo quasi constant curvature, integral curves of the vector field ξ are geodesic and ξ is a proper concircular ...

Let $(M,g)$ be a Riemannian manifold and $(TM,\tilde{g})$ its tangent bundle with the $g-$natural metric. In this paper, family of metallic structures $J$ is constructed on $TM,$ found conditions under which these are integrable. It proved that $(TM,\tilde{g},J)$ decomposable if only flat.

In this paper we prove that a conformally compact Einstein manifold with the round sphere as its conformal infinity has to be the hyperbolic space. We do not assume the manifolds to be spin, but our approach relies on the positive mass theorem for asymptotic flat manifolds. The proof is based on understanding of positive eigenfunctions and compactifications obtained by positive eigenfunctions. ...

Let $G$ be a linear Lie group acting properly on $G$-$\mathrm{spin}^c$ manifold $M$ with compact quotient. We give short proof that Poincaré duality holds between $G$-equivariant $K$-theory of $M$, defined using finite-dimensional $G$-vector bundles, and $K$-homology through the geometric model Baum Douglas.

The one dimension computational model of a sequential injection engine, which runs on compressed natural gas (CNG) with spark ignition, is developed for this study, to simulate the performance of gas flow pressure profile, under various speed conditions. The computational model is used to simulate and study of the steady state and transient processes of the intake manifold. The sequential injec...