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Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds

Year 2025, Volume: 74 Issue: 1, 117 - 129

Abstract

In this article, firstly we study pointwise slant, pointwise hemi-slant submanifolds whose ambient spaces are para-cosymplectic manifolds and we prove that there exist pointwise hemi-slant nontrivial warped product submanifolds whose ambient spaces are para-cosymplectic manifolds by giving some examples. We get several theorems and some characterizations. Later, we also obtain some inequalities.

References

  • Alegre, P., Carriazo, A., Slant submanifolds of para Hermitian manifolds, Mediterr. J. Math., 14 (2017), 214-221. https://doi.org/10.1007/S00009-017-1018-3
  • Ayaz, S., Gündüzalp, Y., Warped product pointwise hemi-slant submanifolds whose ambient spaces are nearly para-Kaehler manifolds, Turk. J. Math., 48(3) (2024), 477-497. https://doi.org/10.55730/1300-0098.3520
  • Bishop, R. L., O’neill, B., Manifolds of negative curvature, Trans Amer. Math. Soc., 145 (1969), 1-9.
  • Chen, B. Y., Garay, O. J., Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math., 36 (2012), 630-640.
  • Gulbahar, M., Kılıç, E., Celik, S. S., Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math., 39 (2015), 884-899.
  • Hiepko, S., Eine innere Kennzeichnung der verzeten Producte, Math. Ann., 241 (1979), 209-215. https://eudml.org/doc/163263
  • Park, K. S., Pointwise slant and pointwise semi-slant submanifolds in almost contact metric manifolds, Mathematics, 13 (2020), 1-33.
  • Prasad, R., Akyol, M. A., Verma, S. K., Kumar, S., Quasi bi-slant submanifolds of Kaehler manifolds, International Electronic Journal of Geometry, 15(1) (2022), 57-68.
  • Sahin, B., Warped product submanifolds Kaehler manifolds with a slant factor, Ann. Polon. Math., 95(3) (2009), 207-226. https://doi.org/10.4064/ap95-3-2
  • Sato, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30(3) (1976), 219-224.
  • Uddin, S., Khan, V. A., Khan, K. A., A note on warped product submanifolds of cosymplectic manifolds, Filomat, 24 (2010), 95-102.
  • Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36(1) (2009), 37-60.
Year 2025, Volume: 74 Issue: 1, 117 - 129

Abstract

References

  • Alegre, P., Carriazo, A., Slant submanifolds of para Hermitian manifolds, Mediterr. J. Math., 14 (2017), 214-221. https://doi.org/10.1007/S00009-017-1018-3
  • Ayaz, S., Gündüzalp, Y., Warped product pointwise hemi-slant submanifolds whose ambient spaces are nearly para-Kaehler manifolds, Turk. J. Math., 48(3) (2024), 477-497. https://doi.org/10.55730/1300-0098.3520
  • Bishop, R. L., O’neill, B., Manifolds of negative curvature, Trans Amer. Math. Soc., 145 (1969), 1-9.
  • Chen, B. Y., Garay, O. J., Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math., 36 (2012), 630-640.
  • Gulbahar, M., Kılıç, E., Celik, S. S., Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math., 39 (2015), 884-899.
  • Hiepko, S., Eine innere Kennzeichnung der verzeten Producte, Math. Ann., 241 (1979), 209-215. https://eudml.org/doc/163263
  • Park, K. S., Pointwise slant and pointwise semi-slant submanifolds in almost contact metric manifolds, Mathematics, 13 (2020), 1-33.
  • Prasad, R., Akyol, M. A., Verma, S. K., Kumar, S., Quasi bi-slant submanifolds of Kaehler manifolds, International Electronic Journal of Geometry, 15(1) (2022), 57-68.
  • Sahin, B., Warped product submanifolds Kaehler manifolds with a slant factor, Ann. Polon. Math., 95(3) (2009), 207-226. https://doi.org/10.4064/ap95-3-2
  • Sato, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30(3) (1976), 219-224.
  • Uddin, S., Khan, V. A., Khan, K. A., A note on warped product submanifolds of cosymplectic manifolds, Filomat, 24 (2010), 95-102.
  • Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36(1) (2009), 37-60.
There are 12 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Articles
Authors

Sedat Ayaz 0000-0002-8225-5503

Yılmaz Gündüzalp 0000-0002-0932-949X

Publication Date
Submission Date June 28, 2024
Acceptance Date December 31, 2024
Published in Issue Year 2025 Volume: 74 Issue: 1

Cite

APA Ayaz, S., & Gündüzalp, Y. (n.d.). Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(1), 117-129.
AMA Ayaz S, Gündüzalp Y. Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 74(1):117-129.
Chicago Ayaz, Sedat, and Yılmaz Gündüzalp. “Geometry of Pointwise Hemi-Slant Warped Product Submanifolds in Para-Contact Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74, no. 1 n.d.: 117-29.
EndNote Ayaz S, Gündüzalp Y Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 1 117–129.
IEEE S. Ayaz and Y. Gündüzalp, “Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 1, pp. 117–129.
ISNAD Ayaz, Sedat - Gündüzalp, Yılmaz. “Geometry of Pointwise Hemi-Slant Warped Product Submanifolds in Para-Contact Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/1 (n.d.), 117-129.
JAMA Ayaz S, Gündüzalp Y. Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.;74:117–129.
MLA Ayaz, Sedat and Yılmaz Gündüzalp. “Geometry of Pointwise Hemi-Slant Warped Product Submanifolds in Para-Contact Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 1, pp. 117-29.
Vancouver Ayaz S, Gündüzalp Y. Geometry of pointwise hemi-slant warped product submanifolds in para-contact manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 74(1):117-29.

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

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