Let U be a real form of a complex semisimple Lie group, and τ , σ, a pair of commuting involutions on U . This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and describe how to produce solutions from curved flats. The solutions are shown to correspond to various special submanifolds, depending on which homogeneous space U/L on...

We prove analogs of Thom’s transversality theorem and Whitney’s theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a Banach manifold. MSC: 32H02, 53C15.

The Kervaire invariant is a Z=2-invariant of framed manifolds of dimension n = 4k + 2. W. Browder proved 5] that this invariant necessarily vanishes if n + 2 is not a power of 2. We give a geometrical proof of this result using a characterization of the Kervaire invariant in terms of multiple points of immersions.

We prove that a sequence of, possibly branched, weak immersions of the two-sphere S into an arbitrary compact riemannian manifold (M, h) with uniformly bounded area and uniformly bounded L−norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a subsequence, to a Lipschitz mapping of S and whose image is made of a connected union of f...

We show that the cobordism group of fold maps of even non-positive codimension q into a manifold N is a sum of q/2 cobordism groups of framed immersions into N and a group related to diffeomorphism groups of manifolds of dimension q + 1. In the case of maps of odd non-positive codimension q, we show that the cobordism groups of fold maps split off (q − 1)/2 cobordism groups of framed immersions.

We give three formulas expressing the Smale invariant of an immersion f of a (4k− 1)-sphere into (4k + 1)-space. The terms of the formulas are geometric characteristics of any generic smooth map g of any oriented 4k-dimensional manifold, where g restricted to the boundary is an immersion regularly homotopic to f in (6k − 1)-space. The formulas imply that if f and g are two non-regularly homotop...

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in Sn×R or Hn×R in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isometric minimal deformations of a given minimal surface in S ×R or H × R, obtained by r...

We establish necessary and sufficient conditions for existence of isometric immersions of a simply connected Riemannian manifold into a two-step nilpotent Lie group. This comprises the case of immersions into H-type groups. MSC 2000: 53C42, 53C30

The pure braid group Γ of a quadruply-punctured Riemann sphere acts on the SL(2, C)-moduli M of the representation variety of such sphere. The points in M are classified into Γ-orbits. We show that, in this case, the monodromy groups of many explicit solutions to the Riemann-Hilbert problem are subgroups of SU(2). Most of these solutions are examples of representations that have dense images in...

Forensic accounting comes under the category of relatively new profession that utilizes various methodologies andimplementation techniques. This field forensic science is structured and constructed by keeping inmind world’s economy, society legislation. With increasing number in financial deceptionsand frauds global has become tagged as savior for safety forthe administration process academic, ...