TY - JOUR
T1 - Erratum to "The geometry of hemi-slant submanifolds of a locally product Riemannian manifold"
AU - Taştan, Hakan Mete
AU - Özdemir, Fatma
N1 - Publisher Copyright:
© Tübi˙tak.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85007174647&partnerID=8YFLogxK
U2 - 10.3906/mat-1509-10
DO - 10.3906/mat-1509-10
M3 - Comment/debate
AN - SCOPUS:85007174647
SN - 1300-0098
VL - 40
SP - 1401
JO - Turkish Journal of Mathematics
JF - Turkish Journal of Mathematics
IS - 6
ER -