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Some remarks on the nonorientable surfaces
Glendon College, York University, Toronto.
Department of Mathematics, University of Bucharest.
1998 (English)In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 63, no 77, p. 47-54Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
1998. Vol. 63, no 77, p. 47-54
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-12925Local ID: c1254af0-b2d0-11db-bf9d-000ea68e967bOAI: oai:DiVA.org:ltu-12925DiVA, id: diva2:985876
Note
Godkänd; 1998; 20070202 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-21Bibliographically approved

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