A new expression for the density of totally geodesic submanifolds in space forms, with stereological applications |
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Authors: | X Gual-Arnau LM Cruz-Orive |
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Institution: | a Departamento de Matemáticas, Universitat Jaume I, 12071 Castelló, Spain b Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain |
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Abstract: | Integral section formulae for totally geodesic submanifolds (planes) intersecting a compact submanifold in a space form are available from appropriate representations of the motion invariant density (measure) of these planes. Here we present a new decomposition of the invariant density of planes in space forms. We apply the new decomposition to rewrite Santaló's sectioning formula and thereby to obtain new mean values for lines meeting a convex body. In particular we extend to space forms a recently published stereological formula valid for isotropic plane sections through a fixed point of a convex body in R3. |
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Keywords: | 53C65 52A55 52A38 |
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