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Integral geometry under cut loci in compact symmetric spaces

Published online by Cambridge University Press:  22 January 2016

Hiroyuki Tasaki
Hiroyuki Tasaki*
Affiliation:
Institute of Mathematics University of Tsukuba, Tsukuba, Ibaraki 305, Japan e-mail: tasaki@math.tsukuba.ac.jp
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The theory of integral geometry has mainly treated identities between integral invariants of submanifolds in Riemannian homogeneous spaces like as dμg(g) where M and N are submanifolds in a Riemannian homogeneous spaces of a Lie group G and I(M ∩ gN) is an integral invariant of M ∩ gN. For example Poincaré’s formula is one of typical identities in integral geometry, which is as follows. We denote by M(R2 ) the identity component of the group of isometries of the plane R2 with a suitable invariant measure μM(R2).

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 137 , March 1995 , pp. 33 - 53
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

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