• Finite dimensional imbeddings of harmonic spaces

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      https://www.ias.ac.in/article/fulltext/pmsc/108/01/0013-0021

    • Keywords

       

      Harmonic manifolds; eigen spaces; imbeddings; symmetric spaces

    • Abstract

       

      For a noncompact harmonic manifoldM we establish finite dimensionality of the eigensubspacesVγ generated by radial eigenfunctions of the form coshr+c. As a consequence, for such harmonic manifolds, we give an isometric imbedding ofM into (Vγ,B), whereB is a nondegenerate symmetric bilinear indefinite form onVγ (analogous to the imbedding of the real hyperbolic spaceHn into ℝn+1 with the indefinite formQ(x,x)=−x02+Σxi2). This imbedding is minimal in a ‘sphere’ in (Vγ,B). Finally we give certain conditions under whichM is symmetric.

    • Author Affiliations

       

      K Ramachandran1 A Ranjan1

      1. Department of Mathematics, Indian Institute of Technology, Powai, Mumbai - 400 076, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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