Affine analogues of the Sasaki-Shchepetilov connection

Maria Robaszewska. "Affine analogues of the Sasaki-Shchepetilov connection." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 15 (2016): 37-49. <http://eudml.org/doc/287082>.

@article{MariaRobaszewska2016,
abstract = {For two-dimensional manifold M with locally symmetric connection ∇ and with ∇-parallel volume element vol one can construct a flat connection on the vector bundle TM ⊕ E, where E is a trivial bundle. The metrizable case, when M is a Riemannian manifold of constant curvature, together with its higher dimension generalizations, was studied by A.V. Shchepetilov [J. Phys. A: 36 (2003), 3893-3898]. This paper deals with the case of non-metrizable locally symmetric connection. Two flat connections on TM ⊕ (ℝ × M) and two on TM ⊕ (ℝ2 × M) are constructed. It is shown that two of those connections – one from each pair – may be identified with the standard flat connection in ℝN, after suitable local affine embedding of (M,∇) into ℝN.},
author = {Maria Robaszewska},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {connection on a vector bundle; associated vector bundle; connection form; locally symmetric connection},
language = {eng},
pages = {37-49},
title = {Affine analogues of the Sasaki-Shchepetilov connection},
url = {http://eudml.org/doc/287082},
volume = {15},
year = {2016},
}

TY - JOUR
AU - Maria Robaszewska
TI - Affine analogues of the Sasaki-Shchepetilov connection
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2016
VL - 15
SP - 37
EP - 49
AB - For two-dimensional manifold M with locally symmetric connection ∇ and with ∇-parallel volume element vol one can construct a flat connection on the vector bundle TM ⊕ E, where E is a trivial bundle. The metrizable case, when M is a Riemannian manifold of constant curvature, together with its higher dimension generalizations, was studied by A.V. Shchepetilov [J. Phys. A: 36 (2003), 3893-3898]. This paper deals with the case of non-metrizable locally symmetric connection. Two flat connections on TM ⊕ (ℝ × M) and two on TM ⊕ (ℝ2 × M) are constructed. It is shown that two of those connections – one from each pair – may be identified with the standard flat connection in ℝN, after suitable local affine embedding of (M,∇) into ℝN.
LA - eng
KW - connection on a vector bundle; associated vector bundle; connection form; locally symmetric connection
UR - http://eudml.org/doc/287082
ER -