TY - JOUR T1 - Pointwise bi-slant submersions from cosymplectic manifolds AU - Aykurt Sepet, Sezin AU - Ergüt, Mahmut PY - 2020 DA - December Y2 - 2020 DO - 10.31801/cfsuasmas.650697 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 1310 EP - 1319 VL - 69 IS - 2 LA - en AB - We introduce pointwise bi-slant submersions from cosymplectic manifolds onto Riemannian manifolds as a generalization of anti-invariant, semi-invariant, semi-slant, hemi-slant, pointwise semi-slant, pointwise hemi-slant and pointwise slant Riemannian submersions. We give an example for pointwise bi-slant submersions and investigate integrability and totally geodesicness of the distributions which are mentioned in the definition of pointwise bi-slant submersions admitting vertical Reeb vector field. Also we obtain necessary and sufficient conditions for such submersions to be totally geodesic maps. KW - Riemannian submersion KW - pointwise bi-slant submersion KW - cosymplectic manifold CR - Akyol, M.A.,Gündüzalp, Y., Hemi-slant submersions from almost product Riemannian manifolds, Gulf Journal of Mathematics, 4(3) (2016), 15-27. CR - Akyol, M.A., Sarı, R., On semi-slant ξ^{⊥}-Riemannian submersions, Mediterr. J. Math., 14 (2017), 234(20 pp). CR - Akyol, M.A.Sahin, B., Conformal slant submersions, Hacet. J. Math. Stat., 48 (2019), 28-44. CR - Alqahtani, L.S., Stankovic, M.S., Uddin, S., Warped Product Bi-slant Submanifolds of Cosymplectic Manifolds, Filomat, 31(16) (2017), 5065-5071. CR - Aykurt Sepet, S., Ergüt,M., Pointwise slant submersions from cosymplectic manifolds, Turk. J. Math., 40 (2016), 582-593. CR - Baird, P., Wood, J.C., Harmonic morphisms between Riemannian manifolds, London Mathematical Society Monographs, Oxford University Press, Oxford, 2003. CR - Blair, D.E., Contact manifolds in Riemannian geometry, Lectures Notes in Mathematics 509, Springer-Verlag, Berlin, 146p., 1976. CR - Carriazo, A., Bi-slant Immersions, Proceeding of the ICRAMS, (2000), 88-97. CR - Chen, B.Y., Slant immersions, Bull. Austral. Math. Soc., 41(1990), 135-147. CR - Erken, İ.K., Murathan, C., On Slant Riemannian Submersions for Cosymplectic Manifolds, Bull. Korean Math. Soc., (2014), 51, 1749-1771. CR - Etayo, F., On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen, 51 (1998), 217-223. CR - Falcitelli, M., Ianus, S., Pastore, A.M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004. CR - Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737. CR - Gündüzalp, Y., Semi-slant submersions from almost product Riemannian manifolds, Demonstratio Mathematica, 49(3) (2016), 345-356. CR - Gündüzalp, Y., Akyol, M.A., Conformal slant submersions from cosymplectic manifolds, Turk. J. Math., 42 (2018), 2672-2689. CR - Lee, J.W., Şahin, B., Pointwise slant submersions, Bull. Korean Math. Soc., 51(4) (2014), 1115-1126. CR - Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Differential Geom., 4 (1970), 237-244. CR - O'Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13 (1966), 458-469. CR - Sayar, C., Özdemir, F., Taştan, H.M., Pointwise semi-slant submersions whose total manifolds are locally product Riemannian manifolds, International Journal of Maps in Mathematics, 1 (2018), 91-115. CR - Sayar, C., Taştan, H.M., Özdemir, F., Tripathi, M.M., Generic submersions from Kaehlerian Manifolds, Bull. Malays. Math. Sci. Soc., https://doi.org/10.1007/s40840-018-00716-2. CR - Şahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J. Math., 8(3) (2010), 437-447. CR - Şahin, B., Semi-invariant Riemannian submersions from almost Hermitian manifolds, Can. Math. Bull., 56 (2011), 173-183. CR - Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, 54(102) (2011), 93-105. CR - Taştan, H.M., Şahin, B., Yanan, Ş., Hemi-slant submersions, Mediterr. J. Math., 13 (2016), 2171-2184. CR - Tastan, H.M., Lagrangian submersions from normal almost contact manifolds, Filomat, 31(12) (2017), 3885-3895. CR - Tastan, H.M., Gerdan Aydın, S., Clairaut anti-invariant submersions from cosymplectic manifolds, Honam Mathematical J., 41(4) (2019), 707-724. CR - Uddin, S., Chen, B.Y., Al-Solamy, F.R., Warped Product Bi-slant Immersions in Kaehler Manifolds , Mediterr. J. Math, 14(95) (2017). CR - Watson, B., Almost Hermitian submersions, J. Differential Geometry, 11(1) (1976), 147-165. UR - https://doi.org/10.31801/cfsuasmas.650697 L1 - https://dergipark.org.tr/en/download/article-file/861620 ER -