in this paper we study the impact of minkowski metric matrix on a projection in theminkowski space m along with their basic algebraic and geometric properties.the relationbetween the m-projections and the minkowski inverse of a matrix a in the minkowski spacemis derived. in the remaining portion commutativity of minkowski inverse in minkowski spacem is analyzed in terms of m-projections as an a...

In this paper we study the impact of Minkowski metric matrix on a projection in the Minkowski Space M along with their basic algebraic and geometric properties.The relation between the m-projections and the Minkowski inverse of a matrix A in the minkowski space M is derived. In the remaining portion commutativity of Minkowski inverse in Minkowski Space M is analyzed in terms of m-projections as...

We extend the results of [LMT] to the non-symmetric and quasiconvex cases. Namely, we consider finite-dimensional space endowed with gauge of either closed convex body (not necessarily symmetric) or closed symmetric quasi-convex body. We show that if a generic subspace of some fixed proportional dimension of one such space is isomorphic to a generic quotient of some proportional dimension of an...

Inspiration: Simple noncompact connected Lie groups — Irreducible symmetric spaces of noncompact type (E.Cartan et al). Here there is an essentially 1-1 correspondence between algebraic objects (a Lie group of a certain type) and geometric objects (certain symmetric spaces). Namely, given a Lie group G on constructs a symmetric space X = G/K (K is a maximal compact subgroup of G) and, conversel...

A symmetric space is a Riemannian manifold that is “symmetric” about each of its points: for each p ∈M there is an isometry σp of M such that (σp)∗ = −I on TpM . Symmetric spaces and their local versions were studied and classified by E.Cartan in the 1920’s. In 1980 D.Ferus [F2] introduced the concept of symmetric submanifolds of Euclidean space: A submanifold M of R is a symmetric submanifold ...

After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.