The integration of the equations for geodesics of left-invariant metrics on simple Lie groups using special functions
Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 473-485
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This paper studies a multiparameter family of left-invariant metrics on simple Lie groups which generalizes the inertia tensor of an $n$-dimensional rigid body. A class of solutions is produced for the geodesic equations on simple linear groups expressed in terms of quasipolynomials. For groups of complex matrices with determinant one, explicit formulas are found for the matrix elements of geodesics. The matrix elements are polynomials in exponentials and in theta-functions on Riemann surfaces.
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@article{SM_1983_45_4_a4,
author = {M. V. Meshcheryakov},
title = {The integration of the equations for geodesics of left-invariant metrics on simple {Lie} groups using special functions},
journal = {Sbornik. Mathematics},
pages = {473--485},
publisher = {mathdoc},
volume = {45},
number = {4},
year = {1983},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1983_45_4_a4/}
}
TY - JOUR AU - M. V. Meshcheryakov TI - The integration of the equations for geodesics of left-invariant metrics on simple Lie groups using special functions JO - Sbornik. Mathematics PY - 1983 SP - 473 EP - 485 VL - 45 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1983_45_4_a4/ LA - en ID - SM_1983_45_4_a4 ER -
%0 Journal Article %A M. V. Meshcheryakov %T The integration of the equations for geodesics of left-invariant metrics on simple Lie groups using special functions %J Sbornik. Mathematics %D 1983 %P 473-485 %V 45 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1983_45_4_a4/ %G en %F SM_1983_45_4_a4
M. V. Meshcheryakov. The integration of the equations for geodesics of left-invariant metrics on simple Lie groups using special functions. Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 473-485. http://geodesic.mathdoc.fr/item/SM_1983_45_4_a4/