Research Article
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Year 2021, , 313 - 330, 29.10.2021
https://doi.org/10.36890/iejg.845483

Abstract

References

  • [1] Adati, T. : Submanifolds of an almost product Riemanian manifold. Kodai Math J. 4, 327-343 (1981).
  • [2] Al-Solamy, F.R., Khan, M.A.: Warped product submanifolds of Riemannian product manifolds. Hindawi Publishing Corporation Abstract and Applied Analysis. Article ID 724898, 12 pages (2012).
  • [3] Atçeken, M.: Warped product semi-slant submanifolds in locally Riemannian product manifolds. Bull. Austral. Math. Soc. 77 (2), 177-186 (2008).
  • [4] Atçeken, M.: Warped Product semi-invariant submanifolds in locally decomposable Riemannian Manifolds. Hacet. J. Math. Stat. 40 (3), 401–407 (2011).
  • [5] Atçeken, M.: Geometry of warped product semi-invariant submanifolds of a locally Riemannian product manifolds. Serdica Math. J. 35, 273-289 (2009).
  • [6] Bejan, C.L.: Almost semi-invariant submanifolds of locally product Riemannian manifolds. Bull. Math. de la Soc. Sci. Math. de la R. S. de Roumanie Tome. 32 (80), No. 1, 3-9 (1988).
  • [7] Bejancu, A.: Semi-invariant submanifolds of locally product Riemannian manifolds. An. Univ. Timi¸soara Ser. ¸Stiint. Math. Al. 22(1-2), 3-11 (1984).
  • [8] Bishop, R. L., O’Neill, B.: Manifolds of negative curvature. Trans. Amer. Math. Soc. 145(1), 1-49 (1969).
  • [9] Chen, B. Y.: Geometry of warped product submanifolds in Kaehler manifolds. Monatsh Math. 133, 177-195 (2001).
  • [10] Chen, B. Y., Dillen, F.: Optimal Inequalities For Multiply Warped Product Submanifolds. Int. Electron. J. Geom. 1(1), 1-11 (2008).
  • [11] Chen, B.Y.: Differential geometry of warped product manifolds and submanifolds. World Scientific. (2017).
  • [12] Dillen, F., Nölker, S.: Semi-paralellity multi rotation surfaces and the helix property. J. Reine. Angew. Math. 435, 33-63 (1993).
  • [13] Gerdan Aydın, S., Taştan, H. M., Traore, M., Ülker, Y.: Biwarped product submanifolds with a slant base factor. (Preprint).
  • [14] Liu, X., Shao, F. M.: Skew semi-invariant submanifolds of locally product manifold. Portugalie Math. 56, 319-327 (1999).
  • [15] Li, H., Liu, X.: Semi-slant submanifolds of a locally product manifold. Georgian Math. J. 12, 273–282 (2005).
  • [16] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. San Diego (1983).
  • [17] Şahin, B.: Slant submanifolds of an almost product Riemannian manifold. J. Korean Math. Soc. 43, 717-732 (2006).
  • [18] Şahin, B.: Warped Product semi-slant submanifolds of a locally product Riemannian manifold. Studia Sci. Math. Hungar. 46(2), 169–184 (2009).
  • [19] Şahin, B.: Warped product semi-invariant submanifolds of a locally product Riemannian manifold. Bull. Math. Soc. Sci. Math. Roumanie. 49(97), 4, 383-394 (2006).
  • [20] Taştan, H. M.: Warped product skew semi-invariant submanifolds of order 1 of a locally product Riemannian manifold. Turk. J. Math. 39, 453-466 (2015).
  • [21] Taştan, H. M., Özdemir, F.: The geometry of hemi-slant submanifolds of a locally product Riemannian manifold. Turk. J. Math. 39, 268-284 (2015).
  • [22] Uddin, S., Mihai, A., Mihai, I., Al-Jedani, A.: Geometry of bi-warped product submanifolds of locally product Riemannian manifolds. RACSAM. 114(42), (2020). https://doi.org/10.1007/s13398-019-00766-6.
  • [23] Ünal, B.: Multiply warped products. J. Geom. Phys. 34(3), 287-301 (2000).
  • [24] Xu, S., Ni, Y.: Submanifolds of product Riemannian manifolds. Acta Mathematica Scientia. 20B(2), 213-218 (2000).
  • [25] Yano, K., Kon, M.: Structures on manifolds. World Scientific, Singapore (1984).

Multiply Warped Product Generalized Semi-Invariant Submanifolds

Year 2021, , 313 - 330, 29.10.2021
https://doi.org/10.36890/iejg.845483

Abstract

We define generalized semi-invariant submanifolds in locally product Riemannian manifolds. Then we study multiply warped product generalized semi-invariant submanifolds in the same structure. We give an existence theorem for such submanifolds. We also give necessary and sufficient conditions for such a submanifold to be a multiply direct product submanifold. Moreover, we establish a general inequality for such submanifolds.

References

  • [1] Adati, T. : Submanifolds of an almost product Riemanian manifold. Kodai Math J. 4, 327-343 (1981).
  • [2] Al-Solamy, F.R., Khan, M.A.: Warped product submanifolds of Riemannian product manifolds. Hindawi Publishing Corporation Abstract and Applied Analysis. Article ID 724898, 12 pages (2012).
  • [3] Atçeken, M.: Warped product semi-slant submanifolds in locally Riemannian product manifolds. Bull. Austral. Math. Soc. 77 (2), 177-186 (2008).
  • [4] Atçeken, M.: Warped Product semi-invariant submanifolds in locally decomposable Riemannian Manifolds. Hacet. J. Math. Stat. 40 (3), 401–407 (2011).
  • [5] Atçeken, M.: Geometry of warped product semi-invariant submanifolds of a locally Riemannian product manifolds. Serdica Math. J. 35, 273-289 (2009).
  • [6] Bejan, C.L.: Almost semi-invariant submanifolds of locally product Riemannian manifolds. Bull. Math. de la Soc. Sci. Math. de la R. S. de Roumanie Tome. 32 (80), No. 1, 3-9 (1988).
  • [7] Bejancu, A.: Semi-invariant submanifolds of locally product Riemannian manifolds. An. Univ. Timi¸soara Ser. ¸Stiint. Math. Al. 22(1-2), 3-11 (1984).
  • [8] Bishop, R. L., O’Neill, B.: Manifolds of negative curvature. Trans. Amer. Math. Soc. 145(1), 1-49 (1969).
  • [9] Chen, B. Y.: Geometry of warped product submanifolds in Kaehler manifolds. Monatsh Math. 133, 177-195 (2001).
  • [10] Chen, B. Y., Dillen, F.: Optimal Inequalities For Multiply Warped Product Submanifolds. Int. Electron. J. Geom. 1(1), 1-11 (2008).
  • [11] Chen, B.Y.: Differential geometry of warped product manifolds and submanifolds. World Scientific. (2017).
  • [12] Dillen, F., Nölker, S.: Semi-paralellity multi rotation surfaces and the helix property. J. Reine. Angew. Math. 435, 33-63 (1993).
  • [13] Gerdan Aydın, S., Taştan, H. M., Traore, M., Ülker, Y.: Biwarped product submanifolds with a slant base factor. (Preprint).
  • [14] Liu, X., Shao, F. M.: Skew semi-invariant submanifolds of locally product manifold. Portugalie Math. 56, 319-327 (1999).
  • [15] Li, H., Liu, X.: Semi-slant submanifolds of a locally product manifold. Georgian Math. J. 12, 273–282 (2005).
  • [16] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. San Diego (1983).
  • [17] Şahin, B.: Slant submanifolds of an almost product Riemannian manifold. J. Korean Math. Soc. 43, 717-732 (2006).
  • [18] Şahin, B.: Warped Product semi-slant submanifolds of a locally product Riemannian manifold. Studia Sci. Math. Hungar. 46(2), 169–184 (2009).
  • [19] Şahin, B.: Warped product semi-invariant submanifolds of a locally product Riemannian manifold. Bull. Math. Soc. Sci. Math. Roumanie. 49(97), 4, 383-394 (2006).
  • [20] Taştan, H. M.: Warped product skew semi-invariant submanifolds of order 1 of a locally product Riemannian manifold. Turk. J. Math. 39, 453-466 (2015).
  • [21] Taştan, H. M., Özdemir, F.: The geometry of hemi-slant submanifolds of a locally product Riemannian manifold. Turk. J. Math. 39, 268-284 (2015).
  • [22] Uddin, S., Mihai, A., Mihai, I., Al-Jedani, A.: Geometry of bi-warped product submanifolds of locally product Riemannian manifolds. RACSAM. 114(42), (2020). https://doi.org/10.1007/s13398-019-00766-6.
  • [23] Ünal, B.: Multiply warped products. J. Geom. Phys. 34(3), 287-301 (2000).
  • [24] Xu, S., Ni, Y.: Submanifolds of product Riemannian manifolds. Acta Mathematica Scientia. 20B(2), 213-218 (2000).
  • [25] Yano, K., Kon, M.: Structures on manifolds. World Scientific, Singapore (1984).
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Moctar Traore 0000-0003-2132-789X

Hakan Mete Taştan 0000-0002-0773-9305

Sibel Gerdan Aydın 0000-0001-5278-6066

Publication Date October 29, 2021
Acceptance Date September 13, 2021
Published in Issue Year 2021

Cite

APA Traore, M., Taştan, H. M., & Gerdan Aydın, S. (2021). Multiply Warped Product Generalized Semi-Invariant Submanifolds. International Electronic Journal of Geometry, 14(2), 313-330. https://doi.org/10.36890/iejg.845483
AMA Traore M, Taştan HM, Gerdan Aydın S. Multiply Warped Product Generalized Semi-Invariant Submanifolds. Int. Electron. J. Geom. October 2021;14(2):313-330. doi:10.36890/iejg.845483
Chicago Traore, Moctar, Hakan Mete Taştan, and Sibel Gerdan Aydın. “Multiply Warped Product Generalized Semi-Invariant Submanifolds”. International Electronic Journal of Geometry 14, no. 2 (October 2021): 313-30. https://doi.org/10.36890/iejg.845483.
EndNote Traore M, Taştan HM, Gerdan Aydın S (October 1, 2021) Multiply Warped Product Generalized Semi-Invariant Submanifolds. International Electronic Journal of Geometry 14 2 313–330.
IEEE M. Traore, H. M. Taştan, and S. Gerdan Aydın, “Multiply Warped Product Generalized Semi-Invariant Submanifolds”, Int. Electron. J. Geom., vol. 14, no. 2, pp. 313–330, 2021, doi: 10.36890/iejg.845483.
ISNAD Traore, Moctar et al. “Multiply Warped Product Generalized Semi-Invariant Submanifolds”. International Electronic Journal of Geometry 14/2 (October 2021), 313-330. https://doi.org/10.36890/iejg.845483.
JAMA Traore M, Taştan HM, Gerdan Aydın S. Multiply Warped Product Generalized Semi-Invariant Submanifolds. Int. Electron. J. Geom. 2021;14:313–330.
MLA Traore, Moctar et al. “Multiply Warped Product Generalized Semi-Invariant Submanifolds”. International Electronic Journal of Geometry, vol. 14, no. 2, 2021, pp. 313-30, doi:10.36890/iejg.845483.
Vancouver Traore M, Taştan HM, Gerdan Aydın S. Multiply Warped Product Generalized Semi-Invariant Submanifolds. Int. Electron. J. Geom. 2021;14(2):313-30.