On geometry of curves of flags of constant type

Boris Doubrov; Igor Zelenko

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1836-1871
  • ISSN: 2391-5455

Abstract

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We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves. The case of classical groups is considered in more detail.

How to cite

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Boris Doubrov, and Igor Zelenko. "On geometry of curves of flags of constant type." Open Mathematics 10.5 (2012): 1836-1871. <http://eudml.org/doc/269813>.

@article{BorisDoubrov2012,
abstract = {We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves. The case of classical groups is considered in more detail.},
author = {Boris Doubrov, Igor Zelenko},
journal = {Open Mathematics},
keywords = {Curves and submanifolds in flag varieties; Equivalence problem; Bundles of moving frames; Graded Lie algebras; Tanaka prolongation; sl2-representations; curves and submanifolds in flag varieties; equivalence problem; bundles of moving frames; graded Lie algebras; -representations},
language = {eng},
number = {5},
pages = {1836-1871},
title = {On geometry of curves of flags of constant type},
url = {http://eudml.org/doc/269813},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Boris Doubrov
AU - Igor Zelenko
TI - On geometry of curves of flags of constant type
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1836
EP - 1871
AB - We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves. The case of classical groups is considered in more detail.
LA - eng
KW - Curves and submanifolds in flag varieties; Equivalence problem; Bundles of moving frames; Graded Lie algebras; Tanaka prolongation; sl2-representations; curves and submanifolds in flag varieties; equivalence problem; bundles of moving frames; graded Lie algebras; -representations
UR - http://eudml.org/doc/269813
ER -

References

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