On the quaternion projective space

Abstract

Apart from being a vital and exciting field in mathematics with interesting results, projective
spaces have various applications in design theory, coding theory, physics, combinatorics, number
theory and extremal combinatorial problems. In this paper, we consider real, complex and
quaternion projective spaces. We focus on the geometric feature of the sectional curvatures. We
first study the real and complex projective spaces. We prove that their sectional curvatures are
constant. Then, we consider the quaternion projective space. Specifically, we prove that the
quaternion projective space has a positive constant sectional curvature. We also determine the
pinching constant for the complex and quaternion projective spaces