Spin structures have wide applications to mathematical physics, in particular to quantum field theory. For the special class Spin(7) geometry, there are different approaches. One of them is constructed by holonomy groups. According to the Berger classification (1955), the Spin(7) group is one of these holonomy classes. Firstly, it presents its properties. After that, vector fields on Spin(7) manifolds will be geometrically introduced. Let M be an 8-dimensional manifold with the Riemannian metric g and structure group G ⊂ SO(8). The structure group G ⊂ Spin(7), then it is called M admits Spin(7)-structure. In general, manifolds with torsion-free are studied. Manifolds admitting Spin(7)-structures with torsion have rich geometry as well. Locally conformal parallel structures have been studied for a long time with Kahler condition being the oldest one. By means of further groups whose holonomy is exceptional, the choices of the G2 and Spin(7) deserve to attention. Ivanov introduces a condition when an 8-dimensional manifold admits a locally conformal parallel Spin(7) structure. Salur and Yalcinkaya studied an almost symplectic structure on Spin(7)-manifold with a 2-plane field. Then, Fowdar studied Spin(7) metrics from Kahler geometry. In this research, we introduce an 8-manifold equipped with a locally conformal Spin(7)-structure with a 2-plane field. Then, some almost Hermitian 6-manifolds can be classified by the structure of M.

Zoom link: https://rochester.zoom.us/j/94706402472