Integral Springer Theorem for Quaternionic Forms

Mercer’s Theorem for Quaternionic Kernels

the series being uniformly and absolutely convergent in (x,y). A number of generalisations to Mercer’s theorem may be found in the literature, in particular dealing with kernels K : Y × Y → C for various choices of Y . However there would appear to have been (to the best of the author’s knowledge) no attempts made to extend Mercer’s theorem to cover non-complex valued kernels. In the present pa...

The Artin-springer Theorem for Quadratic Forms over Semi-local Rings with Finite Residue Fields

Let R be a commutative and unital semi-local ring in which 2 is invertible. In this note, we show that anisotropic quadratic spaces over R remain anisotropic after base change to any odd-degree finite étale extension of R. This generalization of the classical Artin-Springer theorem (concerning the situation where R is a field) was previously established in the case where all residue fields of R...

A rigidity theorem for quaternionic Kähler structures

We study the moduli space of quaternionic Kähler structures on a compact manifold of dimension 4n ≥ 12 from a point of view of Riemannian geometry, not twistor theory. Then we obtain a rigidity theorem for quaternionic Kähler structures of nonzero scalar curvature by observing the moduli space.

Almost quaternionic integral submanifolds and totally umbilic integral submanifolds

In literature (Kobayashi and Nomizu, 1963, 1969; Yano and Ako, 1972; Ishihara, 1974; Özdemir, 2006; Alagöz et al., 2012), almost complex and almost quaternionic structures have been investigated widely. These structures are special structures on the tangent bundle of a manifold. A detailed review can be found in Kirichenko and Arseneva (1997). Let us recall some basic facts and definitions from...

Vector valued hermitian and quaternionic modular forms