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Year 2020, Volume: 69 Issue: 2, 1310 - 1319, 31.12.2020
https://doi.org/10.31801/cfsuasmas.650697

Abstract

References

  • Akyol, M.A.,Gündüzalp, Y., Hemi-slant submersions from almost product Riemannian manifolds, Gulf Journal of Mathematics, 4(3) (2016), 15-27.
  • Akyol, M.A., Sarı, R., On semi-slant ξ^{⊥}-Riemannian submersions, Mediterr. J. Math., 14 (2017), 234(20 pp).
  • Akyol, M.A.Sahin, B., Conformal slant submersions, Hacet. J. Math. Stat., 48 (2019), 28-44.
  • Alqahtani, L.S., Stankovic, M.S., Uddin, S., Warped Product Bi-slant Submanifolds of Cosymplectic Manifolds, Filomat, 31(16) (2017), 5065-5071.
  • Aykurt Sepet, S., Ergüt,M., Pointwise slant submersions from cosymplectic manifolds, Turk. J. Math., 40 (2016), 582-593.
  • Baird, P., Wood, J.C., Harmonic morphisms between Riemannian manifolds, London Mathematical Society Monographs, Oxford University Press, Oxford, 2003.
  • Blair, D.E., Contact manifolds in Riemannian geometry, Lectures Notes in Mathematics 509, Springer-Verlag, Berlin, 146p., 1976.
  • Carriazo, A., Bi-slant Immersions, Proceeding of the ICRAMS, (2000), 88-97.
  • Chen, B.Y., Slant immersions, Bull. Austral. Math. Soc., 41(1990), 135-147.
  • Erken, İ.K., Murathan, C., On Slant Riemannian Submersions for Cosymplectic Manifolds, Bull. Korean Math. Soc., (2014), 51, 1749-1771.
  • Etayo, F., On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen, 51 (1998), 217-223.
  • Falcitelli, M., Ianus, S., Pastore, A.M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
  • Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737.
  • Gündüzalp, Y., Semi-slant submersions from almost product Riemannian manifolds, Demonstratio Mathematica, 49(3) (2016), 345-356.
  • Gündüzalp, Y., Akyol, M.A., Conformal slant submersions from cosymplectic manifolds, Turk. J. Math., 42 (2018), 2672-2689.
  • Lee, J.W., Şahin, B., Pointwise slant submersions, Bull. Korean Math. Soc., 51(4) (2014), 1115-1126.
  • Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Differential Geom., 4 (1970), 237-244.
  • O'Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13 (1966), 458-469.
  • 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.
  • 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.
  • Şahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J. Math., 8(3) (2010), 437-447.
  • Şahin, B., Semi-invariant Riemannian submersions from almost Hermitian manifolds, Can. Math. Bull., 56 (2011), 173-183.
  • Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, 54(102) (2011), 93-105.
  • Taştan, H.M., Şahin, B., Yanan, Ş., Hemi-slant submersions, Mediterr. J. Math., 13 (2016), 2171-2184.
  • Tastan, H.M., Lagrangian submersions from normal almost contact manifolds, Filomat, 31(12) (2017), 3885-3895.
  • Tastan, H.M., Gerdan Aydın, S., Clairaut anti-invariant submersions from cosymplectic manifolds, Honam Mathematical J., 41(4) (2019), 707-724.
  • Uddin, S., Chen, B.Y., Al-Solamy, F.R., Warped Product Bi-slant Immersions in Kaehler Manifolds , Mediterr. J. Math, 14(95) (2017).
  • Watson, B., Almost Hermitian submersions, J. Differential Geometry, 11(1) (1976), 147-165.

Pointwise bi-slant submersions from cosymplectic manifolds

Year 2020, Volume: 69 Issue: 2, 1310 - 1319, 31.12.2020
https://doi.org/10.31801/cfsuasmas.650697

Abstract

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. 

References

  • Akyol, M.A.,Gündüzalp, Y., Hemi-slant submersions from almost product Riemannian manifolds, Gulf Journal of Mathematics, 4(3) (2016), 15-27.
  • Akyol, M.A., Sarı, R., On semi-slant ξ^{⊥}-Riemannian submersions, Mediterr. J. Math., 14 (2017), 234(20 pp).
  • Akyol, M.A.Sahin, B., Conformal slant submersions, Hacet. J. Math. Stat., 48 (2019), 28-44.
  • Alqahtani, L.S., Stankovic, M.S., Uddin, S., Warped Product Bi-slant Submanifolds of Cosymplectic Manifolds, Filomat, 31(16) (2017), 5065-5071.
  • Aykurt Sepet, S., Ergüt,M., Pointwise slant submersions from cosymplectic manifolds, Turk. J. Math., 40 (2016), 582-593.
  • Baird, P., Wood, J.C., Harmonic morphisms between Riemannian manifolds, London Mathematical Society Monographs, Oxford University Press, Oxford, 2003.
  • Blair, D.E., Contact manifolds in Riemannian geometry, Lectures Notes in Mathematics 509, Springer-Verlag, Berlin, 146p., 1976.
  • Carriazo, A., Bi-slant Immersions, Proceeding of the ICRAMS, (2000), 88-97.
  • Chen, B.Y., Slant immersions, Bull. Austral. Math. Soc., 41(1990), 135-147.
  • Erken, İ.K., Murathan, C., On Slant Riemannian Submersions for Cosymplectic Manifolds, Bull. Korean Math. Soc., (2014), 51, 1749-1771.
  • Etayo, F., On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen, 51 (1998), 217-223.
  • Falcitelli, M., Ianus, S., Pastore, A.M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
  • Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737.
  • Gündüzalp, Y., Semi-slant submersions from almost product Riemannian manifolds, Demonstratio Mathematica, 49(3) (2016), 345-356.
  • Gündüzalp, Y., Akyol, M.A., Conformal slant submersions from cosymplectic manifolds, Turk. J. Math., 42 (2018), 2672-2689.
  • Lee, J.W., Şahin, B., Pointwise slant submersions, Bull. Korean Math. Soc., 51(4) (2014), 1115-1126.
  • Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Differential Geom., 4 (1970), 237-244.
  • O'Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13 (1966), 458-469.
  • 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.
  • 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.
  • Şahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J. Math., 8(3) (2010), 437-447.
  • Şahin, B., Semi-invariant Riemannian submersions from almost Hermitian manifolds, Can. Math. Bull., 56 (2011), 173-183.
  • Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, 54(102) (2011), 93-105.
  • Taştan, H.M., Şahin, B., Yanan, Ş., Hemi-slant submersions, Mediterr. J. Math., 13 (2016), 2171-2184.
  • Tastan, H.M., Lagrangian submersions from normal almost contact manifolds, Filomat, 31(12) (2017), 3885-3895.
  • Tastan, H.M., Gerdan Aydın, S., Clairaut anti-invariant submersions from cosymplectic manifolds, Honam Mathematical J., 41(4) (2019), 707-724.
  • Uddin, S., Chen, B.Y., Al-Solamy, F.R., Warped Product Bi-slant Immersions in Kaehler Manifolds , Mediterr. J. Math, 14(95) (2017).
  • Watson, B., Almost Hermitian submersions, J. Differential Geometry, 11(1) (1976), 147-165.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Sezin Aykurt Sepet 0000-0003-1521-6798

Mahmut Ergüt This is me 0000-0002-9098-8280

Publication Date December 31, 2020
Submission Date November 25, 2019
Acceptance Date July 18, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Aykurt Sepet, S., & Ergüt, M. (2020). Pointwise bi-slant submersions from cosymplectic manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1310-1319. https://doi.org/10.31801/cfsuasmas.650697
AMA Aykurt Sepet S, Ergüt M. Pointwise bi-slant submersions from cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1310-1319. doi:10.31801/cfsuasmas.650697
Chicago Aykurt Sepet, Sezin, and Mahmut Ergüt. “Pointwise Bi-Slant Submersions from Cosymplectic Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1310-19. https://doi.org/10.31801/cfsuasmas.650697.
EndNote Aykurt Sepet S, Ergüt M (December 1, 2020) Pointwise bi-slant submersions from cosymplectic manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1310–1319.
IEEE S. Aykurt Sepet and M. Ergüt, “Pointwise bi-slant submersions from cosymplectic manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1310–1319, 2020, doi: 10.31801/cfsuasmas.650697.
ISNAD Aykurt Sepet, Sezin - Ergüt, Mahmut. “Pointwise Bi-Slant Submersions from Cosymplectic Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1310-1319. https://doi.org/10.31801/cfsuasmas.650697.
JAMA Aykurt Sepet S, Ergüt M. Pointwise bi-slant submersions from cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1310–1319.
MLA Aykurt Sepet, Sezin and Mahmut Ergüt. “Pointwise Bi-Slant Submersions from Cosymplectic Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1310-9, doi:10.31801/cfsuasmas.650697.
Vancouver Aykurt Sepet S, Ergüt M. Pointwise bi-slant submersions from cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1310-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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