Curvatures and symmetries of tangent sphere bundles

This paper has two purposes. (1) Holomorphic sectional curvature and ?-sectional curvature of tangent sphere bundles are investigated. In particular, tangent sphere bundles of constant holomorphic sectional curvature or of constant ?-sectional curvature are classified. (2) Hypersurface geometry of tangent sphere bundles is developed. Tangent sphere bundles with pseudo-parallel shape operator or ?-parallel shape operator are classified