Extended cross product in a 3-dimensional almost contact metric manifold with applications to curve theory

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

In this work, we define a new cross product in 3-dimensional almost contact metric manifold and we study the theory of curves using this new cross product in this manifold. Besides, in the works of Baikousis, Blair [1] and Cho et al. [4], we observe that some theorems are incomplete and excessively generalized are thus their alternative proofs presented.

Anahtar Kelimeler:

Sasakian Manifold, Legendre curve, cross product

Extended cross product in a 3-dimensional almost contact metric manifold with applications to curve theory

Keywords:

Sasakian Manifold, Legendre curve, cross product,

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By equation (3.21), we have σb=±1 = 0. From the above equation since σbis not equal to zero, λ must be zero. It is well known that if λ is eigenvalue of h , then−λ is eigenvalue of h [2]. Thus we have h = 0. Using equation (1.4) and (1.3), as a result, we see that the manifold is a Sasakian manifold.