A new expression for the density of totally geodesic submanifolds in space forms, with stereological applications
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http://dx.doi.org/10.1016/j.difgeo.2008.06.013 |
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Title
A new expression for the density of totally geodesic submanifolds in space forms, with stereological applicationsDate
2009Publisher
ElsevierISSN
9262245Bibliographic citation
Differential Geometry and its Application, 27, 1, p. 124-128Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
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 ... [+]
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 R<sup>3</sup>. © 2008 Elsevier B.V. All rights reserved. [-]
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- MAT_Articles [751]