In this chapter, we give Lie's construction of the space of spheres and define the important
notions of oriented contact and parabolic pencils of spheres. This leads ultimately to a …

Problems in submanifold theory have been studied since the invention of calculus and it was
started with differential geometry of plane curves. Owing to his studies of how to draw …

The classification work Isoparametric hypersurfaces with four principal curvatures, and
Isoparametric hypersurfaces with four principal curvatures, II, left unsettled only those …

In this sequel to an earlier article, employing more commutative algebra than previously, we
show that an isoparametric hypersurface with four principal curvatures and multiplicities (3 …

We study extensions of N-wave systems with PT symmetry and describe the types of
(nonlocal) reductions leading to integrable equations invariant under the P (spatial …

A hypersurface M n− 1 in a real space-form R n, S n or H n is isoparametric if it has constant
principal curvatures. For R n and H n, the classification of isoparametric hypersurfaces is …

We investigate n-component systems of conservation laws that possess third-order
Hamiltonian structures of differential-geometric type. The classification of such systems is …

We consider the WDVV associativity equations in the four-dimensional case. These
nonlinear equations of third order can be written as a pair of six-component commuting two …

It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the
matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U (n) …

The Hodge star mean curvature flow on a 3-dimension Riemannian or pseudo-Riemannian
manifold, the geometric Airy flow on a Riemannian manifold, the Schrodingier flow on …