Integral geometry of complex space forms

Details Integral geometry of complex space forms Integral geometry of complex space forms

2012-04-03

arxiv.org/abs/1204.0604v1

Mathematics

Differential Geometry

67 pages

Scientific paper

Using the language of Alesker's theory of valuations on manifolds, a thorough account of the integral geometry of the complex space forms is given. The local kinematic formulas on complex space forms are computed explicitly using algebraic and geometric methods. These formulas yield previously unknown global kinematic formulas on complex projective and complex hyperbolic spaces. As a special case, we recover and extend Gray's tube formulas and put them into a more conceptual setting. Some basic facts about integral geometry in general Riemannian isotropic spaces are also established.

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