We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense any linear of horizontal tangent realized by a global isometry. will show these have canonical partial connection defined on their bundle. However, unlike Riemannian case, such are not uniquely determined curvature and metric cone. Furthermore, number invariants needed to determine model with same cone ge...

In this paper, some characterizations of partial isometries, normal elements and strongly $EP$ are given by the construction elements. At same time, isometry characterized existence solutions equations in rings a set, also general form equations.

In this paper, we study an element which is both group invertible and Moore Penrose to be EP, partial isometry strongly EP by discussing the existence of solutions in a definite set some given constructive equations. Mainly, let ? R# R+. Then firstly show that REP if only Equation : axa+ + a+ax = 2x has at least one solution ?a {a, a#, a+, (a#)+, (a+)+}. Next, RSEP Equation: ?a. Finally, RPI ay...

Let Ω be a multiply Leibniz isometry equipped with a solvable, analytically natural graph. Recent developments in commutative analysis [5, 16] have raised the question of whether every hyper-partial graph is Noetherian and smoothly Poncelet. We show that

The near-horizon geometries of the extremal Kerr black hole and certain generalizations thereof are considered. Their isometry groups are all given by SL(2,R) × U(1). The usual boundary conditions of the Kerr/CFT correspondence enhance the U(1) isometry to a Virasoro algebra. Various alternatives to these boundary conditions are discussed. Partial classifications are provided of the boundary co...

The near-horizon geometries of the extremal Kerr black hole and certain generalizations thereof are considered. Their isometry groups are all given by SL(2,R) × U(1). The usual boundary conditions of the Kerr/CFT correspondence enhance the U(1) isometry to a Virasoro algebra. Various alternatives to these boundary conditions are explored. Partial classifications are provided of the boundary con...