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.

射影空间除了是数学中一个至关重要的且令人兴奋的领域外，还具有有趣的结果，它在设计理论，编码理论，物理，组合论，数论和极值组合问题中也有多种应用。在本文中，我们考虑了实，复和四元数射影空间。我们专注于截面曲率的几何特征。我们首先研究真实和复杂的投影空间。我们证明它们的截面曲率是恒定的。然后，我们考虑四元数射影空间。具体来说，我们证明四元数投影空间具有正的恒定截面曲率。我们还确定了复数和四元数射影空间的收缩常数。