Isotropic hyper-elasticity, altogether with the equilibrium equations and usual boundary conditions, are formulated directly on body ℬ, a three-dimensional compact orientable manifold equipped mass measure. Pearson–Sewell–Beatty pressure potential is recovered, using Poincaré formula. The existence of such requires which as non-holonomic constraints configuration space.

In this paper we introduce the notion of orbit equivalence for semi-group actions and concept generalized linear control system on smooth manifold. We prove that, under certain conditions, a manifold is equivalent to semigroup homogeneous space.

Let M be a connected, simply oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put M×?M?{point}. In this paper we prove that if X× homeomorphic but not necessarily diffeomorphic to M× (more precisely, it carries structure à la Gompf) then can equipped with complete Ricci-flat Riemannian metric. As byproduct of the construction follows metri...

We recall the complex structure on generalized loop spaces Wk,2(S,X), where S is a compact real manifold with boundary and X manifold, prove Hartogs-type extension theorem for holomorphic maps from certain domains in spaces.

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...

This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)kähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.