Integral geometry of complex space forms

• Published in: Geometric and functional analysis Vol. 24; no. 2; pp. 403 - 492
• Main Authors: Bernig, Andreas, Fu, Joseph H. G., Solanes, Gil
• Format: Journal Article
• Language: English
• Published: Basel Springer Basel 01.04.2014
• Subjects: Analysis; Mathematics; Mathematics and Statistics; Isometric Embedding; Curvature Measure; Complex Projective Space; Riemannian Manifold; Integral Geometry

We show how Alesker’s theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hype...