Achieving seamless global coverage is one of the ultimate goals of space-air-ground integrated network, as a part of which High Altitude Platform (HAP) network can provide wide-area coverage. However, deploying a large number of HAPs will lead to severe congestion of existing frequency bands. Spectrum sharing improves spectrum utilization. The coverage performance improvement and interference caused by spectrum sharing need to be investigated. To this end, this paper analyzes the performance of spectrum sharing between HAP network and terrestrial network. We firstly generalize the Poisson Point Process (PPP) to curves, surfaces and manifolds to model the distribution of terrestrial Base Stations (BSs) and HAPs. Then, the closed-form expressions for coverage probability of HAP network and terrestrial network are derived based on differential geometry and stochastic geometry. We verify the accuracy of closed-form expressions by Monte Carlo simulation. The results show that HAP network has less interference to terrestrial network. Low height and suitable deployment density can improve the coverage probability and transmission capacity of HAP network.