The Jordan normal form of higher order Osserman algebraic curvature tensors

Peter Gilkey; Raina Ivanova

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 2, page 231-242
  • ISSN: 0010-2628

Abstract

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We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type ( r , s ) in a vector space of signature ( p , q ) . We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.

How to cite

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Gilkey, Peter, and Ivanova, Raina. "The Jordan normal form of higher order Osserman algebraic curvature tensors." Commentationes Mathematicae Universitatis Carolinae 43.2 (2002): 231-242. <http://eudml.org/doc/249007>.

@article{Gilkey2002,
abstract = {We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type $(r,s)$ in a vector space of signature $(p,q)$. We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.},
author = {Gilkey, Peter, Ivanova, Raina},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {higher order Jacobi operator; Osserman algebraic curvature tensors; Jordan Osserman algebraic curvature tensors; higher order Jacobi operator; Osserman algebraic curvature tensors; Jordan Osserman algebraic curvature tensors},
language = {eng},
number = {2},
pages = {231-242},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The Jordan normal form of higher order Osserman algebraic curvature tensors},
url = {http://eudml.org/doc/249007},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Gilkey, Peter
AU - Ivanova, Raina
TI - The Jordan normal form of higher order Osserman algebraic curvature tensors
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 231
EP - 242
AB - We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type $(r,s)$ in a vector space of signature $(p,q)$. We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.
LA - eng
KW - higher order Jacobi operator; Osserman algebraic curvature tensors; Jordan Osserman algebraic curvature tensors; higher order Jacobi operator; Osserman algebraic curvature tensors; Jordan Osserman algebraic curvature tensors
UR - http://eudml.org/doc/249007
ER -

References

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