Analogies for Compact Two-point Homogeneous Spaces

Valery V. Volchkov and Vitaly V. Volchkov
Additional contact information
Valery V. Volchkov: Donetsk National University, Department of Mathematics
Vitaly V. Volchkov: Donetsk National University, Department of Mathematics

Chapter Chapter 4 in Offbeat Integral Geometry on Symmetric Spaces, 2013, pp 111-134 from Springer

Abstract: Abstract The operators $$ \mathfrak{U}_\delta$$ which we studied in Chapter 3 have analogues in the compact case. In this chapter we study their properties for compact two-point homogeneous spaces of dimension > 1. These are the Riemannian manifolds M with the property that for any two pairs of points $$(p_1,\,p_2)\,{\rm and}\,(q_1,q_2)\,{\rm satisfying}\, d((p_1,\,p_2)\,=\,(q_1,q_2)\,{\rm where}\, d{\rm \,is\, the \,distance \,on}\, M$$ , there exists an isometry mapping $$(p_1\,to\,p_2)\,{\rm and}\,(p_1\,to\,p_2).$$ By virtue of Wang’s classification (see Helgason [H5, Chapter 1 , § 4 ]) these are also the compact symmetric spaces of rank one. Unlike the non-compact case, the treatment in this chapter is based on the realizations of the spaces under consideration. Accordingly, the use of Lie theory is minimal.

Keywords: Symmetric Space; Harmonic Polynomial; Riemannian Symmetric Space; Complex Quadratic; Wiener Theorem (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0572-8_4

Ordering information: This item can be ordered from
http://www.springer.com/9783034805728

DOI: 10.1007/978-3-0348-0572-8_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().