Refine
Document Type
- Article (2)
- Contribution to a Periodical (1)
Has Fulltext
- yes (3)
Is part of the Bibliography
- no (3)
Keywords
- Curvature measure (1)
- Lipschitz–Killing measures (1)
- Pseudo-Riemannian manifolds (1)
- Valuation (1)
- Weyl principle (1)
Institute
- Informatik und Mathematik (2)
- Mathematik (1)
- Präsidium (1)
The recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.
We show the existence of additive kinematic formulas for general flag area measures, which generalizes a recent result by Wannerer. Building on previous work by the second named author, we introduce an algebraic framework to compute these formulas explicitly. This is carried out in detail in the case of the incomplete flag manifold consisting of all (p+1)-planes containing a unit vector.
