Algebraic restrictions on geometric realizations of curvature models

Corey Dunn; Zoë Smith

Archivum Mathematicum (2021)

  • Volume: 057, Issue: 3, page 175-194
  • ISSN: 0044-8753

Abstract

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We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders, and demonstrate that for certain model spaces and realizations, homothety curvature homogeneity implies curvature homogeneity.

How to cite

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Dunn, Corey, and Smith, Zoë. "Algebraic restrictions on geometric realizations of curvature models." Archivum Mathematicum 057.3 (2021): 175-194. <http://eudml.org/doc/298264>.

@article{Dunn2021,
abstract = {We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders, and demonstrate that for certain model spaces and realizations, homothety curvature homogeneity implies curvature homogeneity.},
author = {Dunn, Corey, Smith, Zoë},
journal = {Archivum Mathematicum},
keywords = {curvature model; curvature homogeneous; homothethy curvature homogeneous},
language = {eng},
number = {3},
pages = {175-194},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Algebraic restrictions on geometric realizations of curvature models},
url = {http://eudml.org/doc/298264},
volume = {057},
year = {2021},
}

TY - JOUR
AU - Dunn, Corey
AU - Smith, Zoë
TI - Algebraic restrictions on geometric realizations of curvature models
JO - Archivum Mathematicum
PY - 2021
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 057
IS - 3
SP - 175
EP - 194
AB - We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders, and demonstrate that for certain model spaces and realizations, homothety curvature homogeneity implies curvature homogeneity.
LA - eng
KW - curvature model; curvature homogeneous; homothethy curvature homogeneous
UR - http://eudml.org/doc/298264
ER -

References

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