The Gelfand theorem and its converse in Sasakian geometry
type: Item
instance of: scholarly article
title: The Gelfand theorem and its converse in Sasakian geometry
zbMATH Open document ID: 0644.53042
author: Oldřich Kowalski
author: Lieven Vanhecke
published in: Kodai Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The Gelfand theorem states that for a symmetric space \(M=G/H\), where G denotes the connected component of the identity of the full isometry group of M, the algebra D(G/H) of invariant differential operators is commutative. It is known that the converse of this theorem is not true in general. The authors consider the converse in the case of \(\phi\)- symmetric spaces. Using the group of automorphisms of the Sasakian structure they obtain the commutativity of D(G/H) modulo the characteristic differential operator determined by the characteristic vector field. They also derive a characterization of \(\phi\)-symmetric spaces using the property that all geodesics are orbits of one-parameter subgroups of automorphisms.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4050472
zbMATH Keywords: Gelfand theorem
zbMATH Keywords: symmetric spaces
zbMATH Keywords: Sasakian structure
zbMATH Keywords: geodesics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038821
OpenAlex ID: W2106087896
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DOI: 10.2996/KMJ/1138038821
description: scientific article; zbMATH DE number 4050472