Volume of Domains in Symmetric Spaces*

Abstract

The authors derive a formula for the volume of a compact domain in a symmetricspace from normal sections through a special submanifold in the symmetric space. Thisformula generalizes the volume of classical domains as tubes or domains given as motionsalong the submanifold. Finally, some stereological considerations regarding this formulaare provided.

Keywords

Curvature-adapted submanifold / Lie triple systematic normal bundle / Root decomposable normal bundle / Symmetric space / Volume / 53C35 / 53C21

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