On the Kähler geometry of the Hilbert-Schmidt Grassmannian
type: Item
instance of: scholarly article
title: On the Kähler geometry of the Hilbert-Schmidt Grassmannian
zbMATH Open document ID: 0682.58010
DOI: 10.1007/BF01173699
author: Osmo Pekonen
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155365
review text: In this paper the author considers a geometry of some infinite- dimensional manifolds. He computes the Riemann curvature tensor of the Hilbert-Schmidt Grassmannian endowed with its natural Kähler structure. It is shown that the sectional curvature is non-negative, but not strictly. The author proves also that the sectional curvature of the Hilbert-Schmidt space of almost complex structures is non-positive, but not strictly.
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 4117491
zbMATH Keywords: Kähler geometry
zbMATH Keywords: Riemann curvature
zbMATH Keywords: Hilbert-Schmidt Grassmannian
zbMATH Keywords: Hilbert-Schmidt space
Wikidata QID: Q109936109
reviewed by: Neda Bokan
MaRDI profile type: Publication
cites work: On the Weil-Petersson Metric on Teichmuller Space
cites work: Q3692043
cites work: Sur le théorème de Frobenius
cites work: Superconnection character forms and the Cayley transform
cites work: Q3857325
cites work: On a natural algebraic affine connection on the space of almost complex structures and the curvature of Teichmüller space with respect to its Weil-Petersson metric
description: scientific article; zbMATH DE number 4117491