Araştırma Makalesi
BibTex RIS Kaynak Göster

Quasi Bi-Slant Submanifolds of Kaehler Manifolds

Yıl 2022, Cilt: 15 Sayı: 1, 57 - 68, 30.04.2022
https://doi.org/10.36890/iejg.1061786

Öz

In this paper, we introduce the new notion of quasi bi-slant submanifolds of
almost Hermitian manifolds. Necessary and sufficient conditions for the
integrability of distributions which are involved in the definition of such
submanifolds of a Kaehler manifold are obtained. We also investigate the
necessary and sufficient conditions for these submanifolds of Kaehler
manifolds to be totally geodesic and study the geometry of foliations
determined by the above distributions. Finally, we obtain the necessary and
sufficient conditions for a quasi bi-slant submanifold to be local product
Riemannian manifold and also construct some examples of such submanifolds.

Kaynakça

  • [1] Akyol, M. A., Beyendi, S.: A note on quasi bi-slant submanifolds of cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69(2), 1508-1521, 2020.
  • [2] Al- solamy, F. R., Khan, M. A., Uddin, S.: Totally umbilical hemi-slant submanifolds of Kaehler manifolds. Abstr. Appl. Anal. Article ID 987157, 9 pages, (2011).
  • [3] Bagewadi, C.S., Nirmala, D., Siddesha, M. S.: Semi-invariant submanifolds of (LCS)N-manifold. Communications of the Korean Mathematical Society 33(4), 1331-1339 (2018).
  • [4] Benjancu, A., Papaghuic, N.: Semi-invariant Submanifolds of a Sasakian manifold. An. St. Univ. AI. I. Cuza. Iasi. Math.(N.S.) 27, 163-170 (1981).
  • [5] Blaga, A. M.: Invariant, anti-invariant and slant submanifolds of para-Kenmotsu manifold. BSG Publ. 24, 125-138 (2017).
  • [6] Blair, D. E.: Contact manifold in Riemannian geometry, Lecture notes in Math. 509, Springer-Verlag, New-York (1976).
  • [7] Cabrerizo, J. L., Carriazo, A., Fernandez, L.M., Slant submanifolds in Sasakian manifolds. Glasg. Math. J. 42, 125-138 (2000).
  • [8] Chen, B. Y.: Geometry of slant submanifolds, Katholieke Universiteit, Leuven (1990).
  • [9] Chen, B. Y.: Slant immersions. Bull. Austral. Math. Soc. 41(1), 135-147 (1990).
  • [10] Cortes, V., Mayer, C., Mohaupt, T., Saueres, F.: Special geometry of Euclidean supersymmetry 1. vector multiplets. J. High Energy Phys. 03-028 (2004).
  • [11] De, U. C., Shaikh, A. A.: Complex manifolds and Contact manifolds, Narosa Publ. House, 2009.
  • [12] Etayo, F.: On quasi-slant submanifolds of an almost Hermitian manifold. Publ. Math. Debrecen 53, 217–223 (1998).
  • [13] Kon, M.: Remarks on anti-invariant submanifolds of a Sasakian manifold. Tensor (N.S.) 30, 239-245 (1976).
  • [14] Lotta, A.: Slant submanifold in contact geometry. Bull. Math. Soc. Romanie 39, 183-198 (1996).
  • [15] Papaghuic, N.: Semi-slant submanifold of Kaehlerian manifold. An. St. Univ. Al. I. Cuza. Iasi. Math.(N.S.) 9, 55-61 (1994).
  • [16] Perktaş, S. Y., Blaga, A. M., Kılıç, E.: Almost bi-slant submanifolds of an almost contact metric manifold. Journal of Geometry, 112(2), (2021).
  • [17] Şahin, B.: Warped product submanifolds of a Kaehler manifold with a slant factor. Ann. Pol. Math., 95, 107-126 (2009).
  • [18] Şahin, F.: Cohomology of hemi-slant submanifolds of a Kaehler manifolds. J. Adv. Studies Topology, 5, 27-31 (2014).
  • [19] Uddin, S., Chen, B. Y., Al-Solamy, F. R.: Warped product bi-slant immersions in Kaehler manifolds. Mediterr. J. Math. 14(2), 14-95 (2017).
  • [20] Tashiro, Y.: On contact structures of Hypersurfaces in Almost complex manifolds I. Tohoku Math. J., 15, 62-78 (1963).
  • [21] Taştan, H. M., Özdemir, F.: The geometry of hemi-slant submanifolds of a locally product Riemannian manifold. Turkish Journal of Mathematics, 39 268–284, (2015).
  • [22] Yano, K., Kon, M.: Structures on manifolds, World scientific, 1985.
Yıl 2022, Cilt: 15 Sayı: 1, 57 - 68, 30.04.2022
https://doi.org/10.36890/iejg.1061786

Öz

Kaynakça

  • [1] Akyol, M. A., Beyendi, S.: A note on quasi bi-slant submanifolds of cosymplectic manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69(2), 1508-1521, 2020.
  • [2] Al- solamy, F. R., Khan, M. A., Uddin, S.: Totally umbilical hemi-slant submanifolds of Kaehler manifolds. Abstr. Appl. Anal. Article ID 987157, 9 pages, (2011).
  • [3] Bagewadi, C.S., Nirmala, D., Siddesha, M. S.: Semi-invariant submanifolds of (LCS)N-manifold. Communications of the Korean Mathematical Society 33(4), 1331-1339 (2018).
  • [4] Benjancu, A., Papaghuic, N.: Semi-invariant Submanifolds of a Sasakian manifold. An. St. Univ. AI. I. Cuza. Iasi. Math.(N.S.) 27, 163-170 (1981).
  • [5] Blaga, A. M.: Invariant, anti-invariant and slant submanifolds of para-Kenmotsu manifold. BSG Publ. 24, 125-138 (2017).
  • [6] Blair, D. E.: Contact manifold in Riemannian geometry, Lecture notes in Math. 509, Springer-Verlag, New-York (1976).
  • [7] Cabrerizo, J. L., Carriazo, A., Fernandez, L.M., Slant submanifolds in Sasakian manifolds. Glasg. Math. J. 42, 125-138 (2000).
  • [8] Chen, B. Y.: Geometry of slant submanifolds, Katholieke Universiteit, Leuven (1990).
  • [9] Chen, B. Y.: Slant immersions. Bull. Austral. Math. Soc. 41(1), 135-147 (1990).
  • [10] Cortes, V., Mayer, C., Mohaupt, T., Saueres, F.: Special geometry of Euclidean supersymmetry 1. vector multiplets. J. High Energy Phys. 03-028 (2004).
  • [11] De, U. C., Shaikh, A. A.: Complex manifolds and Contact manifolds, Narosa Publ. House, 2009.
  • [12] Etayo, F.: On quasi-slant submanifolds of an almost Hermitian manifold. Publ. Math. Debrecen 53, 217–223 (1998).
  • [13] Kon, M.: Remarks on anti-invariant submanifolds of a Sasakian manifold. Tensor (N.S.) 30, 239-245 (1976).
  • [14] Lotta, A.: Slant submanifold in contact geometry. Bull. Math. Soc. Romanie 39, 183-198 (1996).
  • [15] Papaghuic, N.: Semi-slant submanifold of Kaehlerian manifold. An. St. Univ. Al. I. Cuza. Iasi. Math.(N.S.) 9, 55-61 (1994).
  • [16] Perktaş, S. Y., Blaga, A. M., Kılıç, E.: Almost bi-slant submanifolds of an almost contact metric manifold. Journal of Geometry, 112(2), (2021).
  • [17] Şahin, B.: Warped product submanifolds of a Kaehler manifold with a slant factor. Ann. Pol. Math., 95, 107-126 (2009).
  • [18] Şahin, F.: Cohomology of hemi-slant submanifolds of a Kaehler manifolds. J. Adv. Studies Topology, 5, 27-31 (2014).
  • [19] Uddin, S., Chen, B. Y., Al-Solamy, F. R.: Warped product bi-slant immersions in Kaehler manifolds. Mediterr. J. Math. 14(2), 14-95 (2017).
  • [20] Tashiro, Y.: On contact structures of Hypersurfaces in Almost complex manifolds I. Tohoku Math. J., 15, 62-78 (1963).
  • [21] Taştan, H. M., Özdemir, F.: The geometry of hemi-slant submanifolds of a locally product Riemannian manifold. Turkish Journal of Mathematics, 39 268–284, (2015).
  • [22] Yano, K., Kon, M.: Structures on manifolds, World scientific, 1985.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Rajendra Prasad 0000-0002-7502-0239

Mehmet Akif Akyol 0000-0003-2334-6955

Sandeep Kumar Verma 0000-0003-2793-0120

Sumeet Kumar 0000-0003-1214-5701

Erken Görünüm Tarihi 30 Nisan 2022
Yayımlanma Tarihi 30 Nisan 2022
Kabul Tarihi 18 Nisan 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 15 Sayı: 1

Kaynak Göster

APA Prasad, R., Akyol, M. A., Verma, S. K., Kumar, S. (2022). Quasi Bi-Slant Submanifolds of Kaehler Manifolds. International Electronic Journal of Geometry, 15(1), 57-68. https://doi.org/10.36890/iejg.1061786
AMA Prasad R, Akyol MA, Verma SK, Kumar S. Quasi Bi-Slant Submanifolds of Kaehler Manifolds. Int. Electron. J. Geom. Nisan 2022;15(1):57-68. doi:10.36890/iejg.1061786
Chicago Prasad, Rajendra, Mehmet Akif Akyol, Sandeep Kumar Verma, ve Sumeet Kumar. “Quasi Bi-Slant Submanifolds of Kaehler Manifolds”. International Electronic Journal of Geometry 15, sy. 1 (Nisan 2022): 57-68. https://doi.org/10.36890/iejg.1061786.
EndNote Prasad R, Akyol MA, Verma SK, Kumar S (01 Nisan 2022) Quasi Bi-Slant Submanifolds of Kaehler Manifolds. International Electronic Journal of Geometry 15 1 57–68.
IEEE R. Prasad, M. A. Akyol, S. K. Verma, ve S. Kumar, “Quasi Bi-Slant Submanifolds of Kaehler Manifolds”, Int. Electron. J. Geom., c. 15, sy. 1, ss. 57–68, 2022, doi: 10.36890/iejg.1061786.
ISNAD Prasad, Rajendra vd. “Quasi Bi-Slant Submanifolds of Kaehler Manifolds”. International Electronic Journal of Geometry 15/1 (Nisan 2022), 57-68. https://doi.org/10.36890/iejg.1061786.
JAMA Prasad R, Akyol MA, Verma SK, Kumar S. Quasi Bi-Slant Submanifolds of Kaehler Manifolds. Int. Electron. J. Geom. 2022;15:57–68.
MLA Prasad, Rajendra vd. “Quasi Bi-Slant Submanifolds of Kaehler Manifolds”. International Electronic Journal of Geometry, c. 15, sy. 1, 2022, ss. 57-68, doi:10.36890/iejg.1061786.
Vancouver Prasad R, Akyol MA, Verma SK, Kumar S. Quasi Bi-Slant Submanifolds of Kaehler Manifolds. Int. Electron. J. Geom. 2022;15(1):57-68.