Some Remarks on the Nonorientable Surfaces
Publications de l'Institut Mathématique, _N_S_63 (1998) no. 77, p. 47
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It is a classical result of F. Klein that for any
nonorientable (regular enough) surface $\boldkey X $ there is an orientable
surface ${\Cal O}_2$ and an involution without fixed point of
${\Cal O}_2$ such that $\boldkey X $ is isomorphic to the quotient space of
${\Cal O}_2$ with respect to the group generated by the respective
involution.
In this note a reinforcement of the Klein's result is presented and the
effect on the vector bundle of covariant tensors of second order on X
produced by that involution is studied.The projection $p:{\Cal O}_2 \longto \boldkey X $ induces an
isomorphism between the vector space of covariant tensors of order two
on $\boldkey X$ and the space of covariant symmetric tensors of order two on
${\Cal O}_2$ which are invariant with respect to the given involution.
@article{PIM_1998_N_S_63_77_a6,
author = {I. Barza and D. Ghisa and Stere Ianus},
title = {Some {Remarks} on the {Nonorientable} {Surfaces}},
journal = {Publications de l'Institut Math\'ematique},
pages = {47 },
publisher = {mathdoc},
volume = {_N_S_63},
number = {77},
year = {1998},
zbl = {1002.53007},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1998_N_S_63_77_a6/}
}
I. Barza; D. Ghisa; Stere Ianus. Some Remarks on the Nonorientable Surfaces. Publications de l'Institut Mathématique, _N_S_63 (1998) no. 77, p. 47 . http://geodesic.mathdoc.fr/item/PIM_1998_N_S_63_77_a6/