In this survey article we introduce the notion of frontals, which provides a class of
generalised submanifolds with singularities but with well-defined tangent spaces. We …

We introduce a type of minimal surface in the pseudo-hyperbolic space H n, n (with n even)
or H n+ 1, n− 1 (with n odd) coming from cyclic SO 0 (n, n+ 1)-Higg bundles. By showing that …

In this paper we study some fundamental algebraic properties of slice functions and slice
regular functions over an alternative $^* $-algebra $ A $ over $\mathbb {R} $. These recently …

We give an explicit geometric structures interpretation of the G 2′-Hitchin component Hit (S,
G 2′)⊂ χ (π 1 S, G 2′) of a closed oriented surface S of genus g≥ 2. In particular, we …

A recent trend in color image processing combines the quaternion algebra with dictionary
learning methods. This paper aims to present a generalization of the quaternion dictionary …

The “dancing metric” is a pseudo-Riemannian metric $\bf {g} $ of signature (2, 2) on the
space $ M^ 4$ of non-incident point-line pairs in the real projective plane $\mathbb {RP} …

It is shown that physical signals and space‐time intervals modeled on split‐octonion
geometry naturally exhibit properties from conventional (3+ 1)‐theory (eg, number of …

Polynomial Almost-Complex Curves in S2,4 Page 1 Polynomial Almost-Complex Curves in S2,4
Parker Evans∗ Abstract For solutions of the g2 affine Toda field equations in C with respect to …

We give a construction that takes a simple linear algebraic group G over a field and
produces a commutative, unital, and simple non-associative algebra A over that field. Two …

There are two well-known parabolic split G 2 geometries in dimension 5,(2, 3, 5)
distributions and G 2 contact structures. Here we link these two geometries with yet another …