Biharmonic Curves in Finsler Spaces

Abstract

Abstract. Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, specific properties and existence of non-geodesic biharmonic curves for some classes of Finsler spaces. Integration of the biharmonic equation is presented for two concrete Finsler metrics.

Classification of f-Biharmonic Curves in Lorentz–Minkowski Space

“…More generally, Sasahara in [3] considered unit biharmonic curves in nonflat Lorentz 3-space forms and obtained full classification of such curves. For the study of biharmonic curves in other model spaces, we refer to [16][17][18][19] with references therein. For some recent progress of biharmonic submanifolds (instead of biharmonic curves), we refer readers to [2, 5, 12-14, 16, 17, 20-24] and the references therein.…”

Untitled

“…Also in (Yıldırım Yılmaz et al 2009, Yıldırım Yılmaz et al 2011, the authors obtained some results for helices of 3dimensional Finsler manifold F 3 . Also Voicu, obtained some characterizations for biharmonic curves in his paper (Voicu, 2014). There are many valuable works and characterizations on helices, Bertrand curves, and biharmonic helices and curves in various spaces (Keleş et al 2010, Körpınar et al 2012, Körpınar et al 2013, Külahcı et al 2008, Külahcı et al 2009, Voicu, 2014, Yüksel Perktaş et al 2012).…”