Research Article
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Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds

Year 2017, , 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, , 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

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.