On the Biharmonic Curves in the Special Linear Group SL(2,R)

We characterize the biharmonic curves in the special linear group SL ( 2 , R ) . In particular, we show that all proper biharmonic curves in SL ( 2 , R ) are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean space R 2 4 .

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 13; no. 1; pp. 443 - 457
Main Authors Onnis, I. I., Passamani, A. Passos
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2016
Subjects
Mathematics
Mathematics and Statistics
53C30
helix curves
58E20
Special linear group
homogeneous spaces
biharmonic curves
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Summary:We characterize the biharmonic curves in the special linear group SL ( 2 , R ) . In particular, we show that all proper biharmonic curves in SL ( 2 , R ) are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean space R 2 4 .
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-014-0474-2