This paper is part of an ongoing program to develop a theory of generalized differential geometry. We consider the space G[X, Y ] of Colombeau generalized functions defined on a manifold X and taking values in a manifold Y . This space is essential in order to study concepts such as flows of generalized vector fields or geodesics of generalized metrics. We introduce an embedding of the space of...

A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami-Kanno super KdV hierarchy and constrained modified super KP hierarchy are investigated from the reduced supersymmetric GelfandDickey brackets. By applying a gauge transformation on the Hamiltonian structures associated with these two...

It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If th...

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.

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...

We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. In particular, given a ĝκ-module that arises as the global sections of a twisted D-module on the affine flag manifold, we show how to compute its untwisted BRST reduction modulo n(K) using the de Rham cohomology of the restrictions to N(K) orbits. A similar relationship holds ...