Research Article
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Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds

Year 2017, Volume: 10 Issue: 2, 73 - 81, 29.10.2017
https://doi.org/10.36890/iejg.545055

Abstract

Recently, the author established a general inequality for doubly warped products in arbitrary
Riemannian manifolds [16]. In the present paper, we obtain similar inequalities for doubly
warped products isometrically immersed in locally conformal almost cosymplectic manifolds.
Some applications are derived.

References

  • [1] Bishop, R. L. and O’Neill, B., Manifolds of negative curvature. Trans. Amer. Math. Soc. 145 (1969), 1-49.
  • [2] Blair, D. E., Contact Manifolds in Riemannian Geometry. Lecture Notes in Math. 509, Springer, Berlin, 1976.
  • [3] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds. Arch. Math. 60 (1993), 568-578.
  • [4] Chen, B. Y., On isometric minimal immersions from warped products into real space forms. Proc. Edinburgh Math. Soc. 45 (2002), 579-587.
  • [5] Chen, B. Y. and Dillen, F., Optimal inequalities for multiply warped product submanifolds. Int. Electron. J. Geom., Vol. 1 (2008), 1-11.
  • [6] Crasmareanu, M., Adapted metrics andWebster curvature on three classes of 3-dimensional geometries. Int. Electron. J. Geom., 7 (2) (2014), 37-46.
  • [7] Malek, F. and Nejadakbary, V.,Warped product submanifold in generalized Sasakian space form. Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 27 no. 2 (2011), 325-338.
  • [8] Matsumoto, K. and Mihai, I., Warped product submanifolds in Sasakian space forms. SUT Journal of Mathematics 38 (2002), 135-144.
  • [9] Matsumoto, K., Mihai, I. and Rosca, R., A certain locally conformal almost cosymplectic manifold and its submanifolds. Tensor N.S. 51 (1) (1992), 91-102.
  • [10] Mihai, A., Warped product submanifolds in complex space forms. Acta Sci. Math. (Szeged) 70 (2004), 419-427.
  • [11] Mihai, A., Warped product submanifolds in quaternion space forms. Rev. Roumaine Math. Pures Appl. 50 (2005), 283-291.
  • [12] Mihai, A., Mihai I. and Miron, R. (Eds.), Topics in Differential Geometry, Ed. Academiei Romane, Bucuresti, 2008.
  • [13] Mihai, I. and Presura, I., An improved Chen first inequality for Legendrian submanifolds in Sasakian space forms. Period. Math. Hung. 74 (2) (2017), 220-226.
  • [14] Murathan, C., Arslan, K., Ezentas, R. and Mihai, I.,Warped product submanifolds in Kenmotsu space forms. Taiwanese J. Math. 10 (2006), 1431-1441.
  • [15] Olszak, Z., Locally conformal almost cosymplectic manifolds. Collq. Math. 57(1) (1989), 73-87.
  • [16] Olteanu, A., A general inequality for doubly warped product submanifolds. Math. J. Okayama Univ. 52 (2010), 133-142.
  • [17] Olteanu, A., Recent results in the geometry of warped product submanifolds, Matrix Rom, 2011.
  • [18] Olteanu, A., Doubly warped product submanifolds in generalized Sasakian space forms, Proceedings RIGA 2014, Ed. Univ. Bucuresti (2014), 174-184.
  • [19] Olteanu, A., Doubly warped products in S-space forms. Rom. J. Math. Comput. Sci. 4 Issue 1 (2014), 111-124.
  • [20] Ünal, B., Doubly warped products. Differ. Geom. App. 15(3) (2001), 253-263.
  • [21] Yoon, D. W., Cho, K. S. and Han, S. G., Some inequalities for warped products in locally conformal almost cosymplectic manifolds. Note Mat. 23 (1) (2004), 51-60.
Year 2017, Volume: 10 Issue: 2, 73 - 81, 29.10.2017
https://doi.org/10.36890/iejg.545055

Abstract

References

  • [1] Bishop, R. L. and O’Neill, B., Manifolds of negative curvature. Trans. Amer. Math. Soc. 145 (1969), 1-49.
  • [2] Blair, D. E., Contact Manifolds in Riemannian Geometry. Lecture Notes in Math. 509, Springer, Berlin, 1976.
  • [3] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds. Arch. Math. 60 (1993), 568-578.
  • [4] Chen, B. Y., On isometric minimal immersions from warped products into real space forms. Proc. Edinburgh Math. Soc. 45 (2002), 579-587.
  • [5] Chen, B. Y. and Dillen, F., Optimal inequalities for multiply warped product submanifolds. Int. Electron. J. Geom., Vol. 1 (2008), 1-11.
  • [6] Crasmareanu, M., Adapted metrics andWebster curvature on three classes of 3-dimensional geometries. Int. Electron. J. Geom., 7 (2) (2014), 37-46.
  • [7] Malek, F. and Nejadakbary, V.,Warped product submanifold in generalized Sasakian space form. Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 27 no. 2 (2011), 325-338.
  • [8] Matsumoto, K. and Mihai, I., Warped product submanifolds in Sasakian space forms. SUT Journal of Mathematics 38 (2002), 135-144.
  • [9] Matsumoto, K., Mihai, I. and Rosca, R., A certain locally conformal almost cosymplectic manifold and its submanifolds. Tensor N.S. 51 (1) (1992), 91-102.
  • [10] Mihai, A., Warped product submanifolds in complex space forms. Acta Sci. Math. (Szeged) 70 (2004), 419-427.
  • [11] Mihai, A., Warped product submanifolds in quaternion space forms. Rev. Roumaine Math. Pures Appl. 50 (2005), 283-291.
  • [12] Mihai, A., Mihai I. and Miron, R. (Eds.), Topics in Differential Geometry, Ed. Academiei Romane, Bucuresti, 2008.
  • [13] Mihai, I. and Presura, I., An improved Chen first inequality for Legendrian submanifolds in Sasakian space forms. Period. Math. Hung. 74 (2) (2017), 220-226.
  • [14] Murathan, C., Arslan, K., Ezentas, R. and Mihai, I.,Warped product submanifolds in Kenmotsu space forms. Taiwanese J. Math. 10 (2006), 1431-1441.
  • [15] Olszak, Z., Locally conformal almost cosymplectic manifolds. Collq. Math. 57(1) (1989), 73-87.
  • [16] Olteanu, A., A general inequality for doubly warped product submanifolds. Math. J. Okayama Univ. 52 (2010), 133-142.
  • [17] Olteanu, A., Recent results in the geometry of warped product submanifolds, Matrix Rom, 2011.
  • [18] Olteanu, A., Doubly warped product submanifolds in generalized Sasakian space forms, Proceedings RIGA 2014, Ed. Univ. Bucuresti (2014), 174-184.
  • [19] Olteanu, A., Doubly warped products in S-space forms. Rom. J. Math. Comput. Sci. 4 Issue 1 (2014), 111-124.
  • [20] Ünal, B., Doubly warped products. Differ. Geom. App. 15(3) (2001), 253-263.
  • [21] Yoon, D. W., Cho, K. S. and Han, S. G., Some inequalities for warped products in locally conformal almost cosymplectic manifolds. Note Mat. 23 (1) (2004), 51-60.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Andreea Olteanu

Publication Date October 29, 2017
Published in Issue Year 2017 Volume: 10 Issue: 2

Cite

APA Olteanu, A. (2017). Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds. International Electronic Journal of Geometry, 10(2), 73-81. https://doi.org/10.36890/iejg.545055
AMA Olteanu A. Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds. Int. Electron. J. Geom. October 2017;10(2):73-81. doi:10.36890/iejg.545055
Chicago Olteanu, Andreea. “Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds”. International Electronic Journal of Geometry 10, no. 2 (October 2017): 73-81. https://doi.org/10.36890/iejg.545055.
EndNote Olteanu A (October 1, 2017) Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds. International Electronic Journal of Geometry 10 2 73–81.
IEEE A. Olteanu, “Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds”, Int. Electron. J. Geom., vol. 10, no. 2, pp. 73–81, 2017, doi: 10.36890/iejg.545055.
ISNAD Olteanu, Andreea. “Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds”. International Electronic Journal of Geometry 10/2 (October 2017), 73-81. https://doi.org/10.36890/iejg.545055.
JAMA Olteanu A. Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds. Int. Electron. J. Geom. 2017;10:73–81.
MLA Olteanu, Andreea. “Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds”. International Electronic Journal of Geometry, vol. 10, no. 2, 2017, pp. 73-81, doi:10.36890/iejg.545055.
Vancouver Olteanu A. Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds. Int. Electron. J. Geom. 2017;10(2):73-81.