Erratum to "The geometry of hemi-slant submanifolds of a locally product Riemannian manifold"

Hakan Mete Taştan*, Fatma Özdemir

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Özet

We realized that in our paper [1] the proof of Theorem 4.8 has two mistakes. Here, we explicitly give some details: Since the tensor field Ω of type (0; 2) defined by Ω(Ū, Ve ) = g(FŪ, V ) is not skew-symmetric, its differential cannot be taken in the usual sense. Moreover, after re-calculation of the equality [inline-equation] (0.1) we see that equation (0.1) does not hold. Therefore, the proof of Theorem 4.8 of [1] is not valid. Then Corollary 4.9 is also not valid. Moreover, equation (4.22) in Corollary 4.9 affects the validity of Theorem 7.1. However, with an additional hypothesis, i.e. "integrability of the anti-invariant distribution [inline-eqaution]⊥" in Corollary 4.9 and Theorem 7.1, these results continue to be true.

Orijinal dilİngilizce
Sayfa (başlangıç-bitiş)1401
Sayfa sayısı1
DergiTurkish Journal of Mathematics
Hacim40
Basın numarası6
DOI'lar
Yayın durumuYayınlandı - 2016

Bibliyografik not

Publisher Copyright:
© Tübi˙tak.

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