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A note on quasi bi-slant submanifolds of cosymplectic manifolds

Year 2020, Volume: 69 Issue: 2, 1508 - 1521, 31.12.2020
https://doi.org/10.31801/cfsuasmas.729545

Abstract

The aim of the present paper is to define and study the notion of quasi bi-slant submanifolds of almost contact metric manifolds. We mainly concerned with quasi bi-slant submanifolds of cosymplectic manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant and quasi hemi-slant submanifolds. First, we give non-trivial examples in order to demostrate the method presented in this paper is effective and investigate the geometry of distributions. Moreover, We study these types of submanifolds with parallel canonical structures.

References

  • Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematic Springer-Verlag, New York, Vol. 509, 1976.
  • Blair, D. E., The theory of quasi-Sasakian structure, J. Differential Geom. 1, (3-4) (1967), 331-345.
  • Carriazo, A., New developments in slant submanifolds theory, Narasa Publishing Hause New Delhi, India, 2002.
  • Carriazo, A., Bi-slant immersions, Proceeding of the ICRAMS 2000, Kharagpur, (2000), 88-97.
  • Chen, B. Y., Geometry of slant submanifolds, Katholieke Universiteit Leuven, Leuven, Belgium, View at Zentralblatt Math., 1990.
  • Chen, B. Y., Slant immersions, Bull. Austral. Math. Soc., 41 (1990), 135-147.
  • Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., Fernandez, M., Slant submanifolds in Sasakian manifolds, Glasgow Math. J., 42 (2000), 125-138.
  • Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., Fernandez, M., Semi-slant submanifolds of a Sasakian manifold, Geom. Dedic., 78(2) (1999), 183-199.
  • Dirik, S., Atçeken, M., On the geometry of pseudo-slant submanifolds of a cosymplectic manifold, International Electronic Journal of Geometry, 9(1) (2016), 45-56.
  • Dirik, S., Atceken, M., Contact pseudo-slant submanifolds of a cosymplectic manifold, New trends in Mathematical Sciences, 6(4) (2018), 154-164.
  • Gupta, R. S., Haider, S. K., Sharfuddin, A. Slant submanifolds in cosymplectic manifolds, Colloquium Mathematicum, 105 (2016), 207-219.
  • Khan, M. A., Totally umbilical hemi slant submanifolds of Cosymplectic manifolds, Mathematica Aeterna, 3(8) (2013), 645-653.
  • Kim, U. K., On anti-invariant submanifolds of cosymplectic manifolds, Bulletin of the Korean Mathematical Society, 21(1) (1984), 35-37.
  • Lone, M. A., Lone, M. S., Shahid, M. H., Hemi-slant submanifolds of cosymplectic manifolds, Cogent Mathematics, 3(1) (2016),1204143.
  • Lotta, A., Slant submanifolds in contact geometry, Bulletin Mathematical Society Roumanie, 39 (1996), 183-198.
  • Ludden, G. D., Submanifolds of cosymplectic manifolds, Journal of Differential Geometry, 4 (1970), 237-244.
  • Olzsak, Z., On almost cosymplectic manifolds, Kodai Math J., 4 (1981), 239-250.
  • Uddin, S., Ozel, C., Khan, V. A., A classication of a totally umbilical slant submanifold of cosymplectic manifolds, Hindawi puplishing corporation abstract applied analysis, article ID 716967, 8 pages (2012).
  • Papaghuic, N., Semi-slant submanifolds of a Kaehlarian manifold, An. St. Univ. Al. I. Cuza. Univ. Iasi, 40 (2009), 55-61. Prasad, R., Verma, S. K., Kumar, S., Quasi hemi-slant submanifolds of sasakian manifolds, Journal of Mathematical and Computational Science, 10(2) (2020), 418-435. Şahin, B., Warped product submanifolds of a Kaehler manifold with a slant factor, Annales Polonici Mathematici, 95 (2009), 107-226.
  • Şahin, B., Slant submanifolds of an almost product Riemannian manifold, Journal of the Korean Mathematical Society, 43(4) (2006), 717-732.
  • Şahin, B., Keleş, S. Slant submanifolds of Kaehler product manifolds, Turkish Journal of Mathematics, 31 (2007), 65-77.
  • Taştan, H. M., Özdemir, F,. The geometry of hemi-slant submanifolds of a locally product Riemannian manifold, Turkish Journal of Mathematics, 39 (2015), 268-284.
Year 2020, Volume: 69 Issue: 2, 1508 - 1521, 31.12.2020
https://doi.org/10.31801/cfsuasmas.729545

Abstract

References

  • Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematic Springer-Verlag, New York, Vol. 509, 1976.
  • Blair, D. E., The theory of quasi-Sasakian structure, J. Differential Geom. 1, (3-4) (1967), 331-345.
  • Carriazo, A., New developments in slant submanifolds theory, Narasa Publishing Hause New Delhi, India, 2002.
  • Carriazo, A., Bi-slant immersions, Proceeding of the ICRAMS 2000, Kharagpur, (2000), 88-97.
  • Chen, B. Y., Geometry of slant submanifolds, Katholieke Universiteit Leuven, Leuven, Belgium, View at Zentralblatt Math., 1990.
  • Chen, B. Y., Slant immersions, Bull. Austral. Math. Soc., 41 (1990), 135-147.
  • Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., Fernandez, M., Slant submanifolds in Sasakian manifolds, Glasgow Math. J., 42 (2000), 125-138.
  • Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., Fernandez, M., Semi-slant submanifolds of a Sasakian manifold, Geom. Dedic., 78(2) (1999), 183-199.
  • Dirik, S., Atçeken, M., On the geometry of pseudo-slant submanifolds of a cosymplectic manifold, International Electronic Journal of Geometry, 9(1) (2016), 45-56.
  • Dirik, S., Atceken, M., Contact pseudo-slant submanifolds of a cosymplectic manifold, New trends in Mathematical Sciences, 6(4) (2018), 154-164.
  • Gupta, R. S., Haider, S. K., Sharfuddin, A. Slant submanifolds in cosymplectic manifolds, Colloquium Mathematicum, 105 (2016), 207-219.
  • Khan, M. A., Totally umbilical hemi slant submanifolds of Cosymplectic manifolds, Mathematica Aeterna, 3(8) (2013), 645-653.
  • Kim, U. K., On anti-invariant submanifolds of cosymplectic manifolds, Bulletin of the Korean Mathematical Society, 21(1) (1984), 35-37.
  • Lone, M. A., Lone, M. S., Shahid, M. H., Hemi-slant submanifolds of cosymplectic manifolds, Cogent Mathematics, 3(1) (2016),1204143.
  • Lotta, A., Slant submanifolds in contact geometry, Bulletin Mathematical Society Roumanie, 39 (1996), 183-198.
  • Ludden, G. D., Submanifolds of cosymplectic manifolds, Journal of Differential Geometry, 4 (1970), 237-244.
  • Olzsak, Z., On almost cosymplectic manifolds, Kodai Math J., 4 (1981), 239-250.
  • Uddin, S., Ozel, C., Khan, V. A., A classication of a totally umbilical slant submanifold of cosymplectic manifolds, Hindawi puplishing corporation abstract applied analysis, article ID 716967, 8 pages (2012).
  • Papaghuic, N., Semi-slant submanifolds of a Kaehlarian manifold, An. St. Univ. Al. I. Cuza. Univ. Iasi, 40 (2009), 55-61. Prasad, R., Verma, S. K., Kumar, S., Quasi hemi-slant submanifolds of sasakian manifolds, Journal of Mathematical and Computational Science, 10(2) (2020), 418-435. Şahin, B., Warped product submanifolds of a Kaehler manifold with a slant factor, Annales Polonici Mathematici, 95 (2009), 107-226.
  • Şahin, B., Slant submanifolds of an almost product Riemannian manifold, Journal of the Korean Mathematical Society, 43(4) (2006), 717-732.
  • Şahin, B., Keleş, S. Slant submanifolds of Kaehler product manifolds, Turkish Journal of Mathematics, 31 (2007), 65-77.
  • Taştan, H. M., Özdemir, F,. The geometry of hemi-slant submanifolds of a locally product Riemannian manifold, Turkish Journal of Mathematics, 39 (2015), 268-284.
There are 22 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Mehmet Akif Akyol 0000-0003-2334-6955

Selahattin Beyendi This is me 0000-0002-1037-6410

Publication Date December 31, 2020
Submission Date April 29, 2020
Acceptance Date October 17, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Akyol, M. A., & Beyendi, S. (2020). A note on quasi bi-slant submanifolds of cosymplectic manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1508-1521. https://doi.org/10.31801/cfsuasmas.729545
AMA Akyol MA, Beyendi S. A note on quasi bi-slant submanifolds of cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1508-1521. doi:10.31801/cfsuasmas.729545
Chicago Akyol, Mehmet Akif, and Selahattin Beyendi. “A Note on Quasi Bi-Slant Submanifolds of Cosymplectic Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1508-21. https://doi.org/10.31801/cfsuasmas.729545.
EndNote Akyol MA, Beyendi S (December 1, 2020) A note on quasi bi-slant submanifolds of cosymplectic manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1508–1521.
IEEE M. A. Akyol and S. Beyendi, “A note on quasi bi-slant submanifolds of cosymplectic manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1508–1521, 2020, doi: 10.31801/cfsuasmas.729545.
ISNAD Akyol, Mehmet Akif - Beyendi, Selahattin. “A Note on Quasi Bi-Slant Submanifolds of Cosymplectic Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1508-1521. https://doi.org/10.31801/cfsuasmas.729545.
JAMA Akyol MA, Beyendi S. A note on quasi bi-slant submanifolds of cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1508–1521.
MLA Akyol, Mehmet Akif and Selahattin Beyendi. “A Note on Quasi Bi-Slant Submanifolds of Cosymplectic Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1508-21, doi:10.31801/cfsuasmas.729545.
Vancouver Akyol MA, Beyendi S. A note on quasi bi-slant submanifolds of cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1508-21.

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

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