A note on quasi bi-slant submanifolds of cosymplectic manifolds

Yıl 2020, Cilt: 69 Sayı: 2, 1508 - 1521, 31.12.2020

Mehmet Akif Akyol Selahattin Beyendi

https://doi.org/10.31801/cfsuasmas.729545

Cited By: 6

Öz

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.

Anahtar Kelimeler

Slant submanifold, , bi-slant submanifold, quasi bi-slant submanifold, cosymplectic manifold

Kaynakça

• 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.