Classification of invariant AHS-structures on semisimple locally symmetric spaces

Jan Gregorovič

Open Mathematics (2013)

  • Volume: 11, Issue: 12, page 2062-2075
  • ISSN: 2391-5455

Abstract

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We discuss which semisimple locally symmetric spaces admit an AHS-structure invariant under local symmetries. We classify them for all types of AHS-structures and determine possible equivalence classes of such AHS-structures.

How to cite

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Jan Gregorovič. "Classification of invariant AHS-structures on semisimple locally symmetric spaces." Open Mathematics 11.12 (2013): 2062-2075. <http://eudml.org/doc/269121>.

@article{JanGregorovič2013,
abstract = {We discuss which semisimple locally symmetric spaces admit an AHS-structure invariant under local symmetries. We classify them for all types of AHS-structures and determine possible equivalence classes of such AHS-structures.},
author = {Jan Gregorovič},
journal = {Open Mathematics},
keywords = {Semisimple locally symmetric space; Invariant geometric structure; Almost hermitian symmetric structure; |1|-graded parabolic geometry; Classification; semisimple locally symmetric space; invariant geometric structure; almost Hermitian symmetric structure; 1-graded parabolic geometry; classification},
language = {eng},
number = {12},
pages = {2062-2075},
title = {Classification of invariant AHS-structures on semisimple locally symmetric spaces},
url = {http://eudml.org/doc/269121},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Jan Gregorovič
TI - Classification of invariant AHS-structures on semisimple locally symmetric spaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 12
SP - 2062
EP - 2075
AB - We discuss which semisimple locally symmetric spaces admit an AHS-structure invariant under local symmetries. We classify them for all types of AHS-structures and determine possible equivalence classes of such AHS-structures.
LA - eng
KW - Semisimple locally symmetric space; Invariant geometric structure; Almost hermitian symmetric structure; |1|-graded parabolic geometry; Classification; semisimple locally symmetric space; invariant geometric structure; almost Hermitian symmetric structure; 1-graded parabolic geometry; classification
UR - http://eudml.org/doc/269121
ER -

References

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  1. [1] Berger M., Les espaces symétriques noncompacts, Ann. Sci. École Norm. Sup., 1957, 74(2), 85–177 
  2. [2] Bertram W., The Geometry of Jordan and Lie Structures, Lecture Notes in Math., 1754, Springer, Berlin, 2000 http://dx.doi.org/10.1007/b76884 Zbl1014.17024
  3. [3] Čap A., Slovák J., Parabolic Geometries I, Math. Surveys Monogr., 154, American Mathematical Society, Providence, 2009 Zbl1183.53002
  4. [4] Gregorovič J., General construction of symmetric parabolic structures, Differential Geom. Appl., 2012, 30(5), 450–476 http://dx.doi.org/10.1016/j.difgeo.2012.06.006 Zbl06092689
  5. [5] Zalabová L., Parabolic symmetric spaces, Ann. Global Anal. Geom., 2010, 37(2), 125–141 http://dx.doi.org/10.1007/s10455-009-9177-5 Zbl1188.53026

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