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An inequality for warped product submanifolds of a locally product Riemannian manifold

Year 2019, Volume 48, Issue 2, 351 - 358, 01.04.2019

Abstract

Recently, Sahin studied the warped product semi-slant submanifolds of locally product Riemannian manifolds. In this paper, we obtain some geometric properties of such submanifolds with an example. Also, we establish a sharp relationship between the squared norm of the second fundamental form and the warping function in terms of the slant angle. The equality case is also considered.

References

  • M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Austral. Math. Soc. 77, 177–186, 2008.
  • M. Atceken, Geometry of warped product semi-invariant submanifolds of a locally Riemannian product manifold, Serdica Math. J. 35, 273–286, 2009.
  • M. Atceken, Warped product semi-invariant submanifolds in locally decomposable Riemannian manifolds, Hacet. J. Math. Stat. 40, 401–407, 2011.
  • A. Bejancu, Semi-invariant submanifolds of locally Riemannian product manifolds, Ann. Univ. Timisoara S. Math. 22, 3–11, 1984.
  • R.L. Bishop and B. O’Neill, Manifolds of Negative curvature, Trans. Amer. Math. Soc. 145, 1–49, 1969.
  • B.Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41, 135–147, 1990.
  • H. Li and X. Li, Semi-slant submanifolds of locally product manifolds, Georgian Math. J. 12, 273–282, 2005.
  • K. Matsumoto, On submanifolds of locally product Riemannian manifolds, TRU Math. 18, 145–157, 1982.
  • N. Papaghiuc, Semi-slant submanifolds of Kaehlerian manifold, Ann. St. Univ. Iasi, 9, 55–61, 1994.
  • B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43, 717–732, 2006.
  • B. Sahin, Warped product semi-invariant submanifolds of locally product Riemannian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome, 49 (97), 383–394, 2006.
  • B. Sahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia Sci. Math. Hungar. 46, 169–184, 2009.
  • S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant submanifolds of cosymplectic manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) Tomul LXII, (f. 2,3), 901–913, 2016.
  • S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian manifolds, Publ. Math. Debrecen, 91 (3-4), 331–348, 2017.
  • S. Uddin, A. Ali, N.M. Al-Asmari and W.A. Othman, Warped product pseudo-slant submanifolds in a locally product Riemannian manifold, Diff. Geometry Dyn. Syst. 18, 147–158, 2016.
  • S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant im- mersions in Kaehler manifolds, Mediterr. J. Math. 14, Art. 95, 1–11, 2017.
  • S. Uddin and A.Y.M. Chi, Warped product pseudo-slant submanifolds of nearly Kaehler manifolds, An. St. Univ. Ovidius Constanta, 19 (3), 195–204, 2011.
  • K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.

Year 2019, Volume 48, Issue 2, 351 - 358, 01.04.2019

Abstract

References

  • M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Austral. Math. Soc. 77, 177–186, 2008.
  • M. Atceken, Geometry of warped product semi-invariant submanifolds of a locally Riemannian product manifold, Serdica Math. J. 35, 273–286, 2009.
  • M. Atceken, Warped product semi-invariant submanifolds in locally decomposable Riemannian manifolds, Hacet. J. Math. Stat. 40, 401–407, 2011.
  • A. Bejancu, Semi-invariant submanifolds of locally Riemannian product manifolds, Ann. Univ. Timisoara S. Math. 22, 3–11, 1984.
  • R.L. Bishop and B. O’Neill, Manifolds of Negative curvature, Trans. Amer. Math. Soc. 145, 1–49, 1969.
  • B.Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41, 135–147, 1990.
  • H. Li and X. Li, Semi-slant submanifolds of locally product manifolds, Georgian Math. J. 12, 273–282, 2005.
  • K. Matsumoto, On submanifolds of locally product Riemannian manifolds, TRU Math. 18, 145–157, 1982.
  • N. Papaghiuc, Semi-slant submanifolds of Kaehlerian manifold, Ann. St. Univ. Iasi, 9, 55–61, 1994.
  • B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43, 717–732, 2006.
  • B. Sahin, Warped product semi-invariant submanifolds of locally product Riemannian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome, 49 (97), 383–394, 2006.
  • B. Sahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia Sci. Math. Hungar. 46, 169–184, 2009.
  • S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant submanifolds of cosymplectic manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) Tomul LXII, (f. 2,3), 901–913, 2016.
  • S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian manifolds, Publ. Math. Debrecen, 91 (3-4), 331–348, 2017.
  • S. Uddin, A. Ali, N.M. Al-Asmari and W.A. Othman, Warped product pseudo-slant submanifolds in a locally product Riemannian manifold, Diff. Geometry Dyn. Syst. 18, 147–158, 2016.
  • S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant im- mersions in Kaehler manifolds, Mediterr. J. Math. 14, Art. 95, 1–11, 2017.
  • S. Uddin and A.Y.M. Chi, Warped product pseudo-slant submanifolds of nearly Kaehler manifolds, An. St. Univ. Ovidius Constanta, 19 (3), 195–204, 2011.
  • K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Falleh R. AL-SOLAMY This is me

0000-0003-3144-570X


Siraj UDDİN> (Primary Author)

0000-0002-3564-6405

Publication Date April 1, 2019
Published in Issue Year 2019, Volume 48, Issue 2

Cite

Bibtex @research article { hujms546354, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, number = {2}, pages = {351 - 358}, title = {An inequality for warped product submanifolds of a locally product Riemannian manifold}, key = {cite}, author = {Al-solamy, Falleh R. and Uddin, Siraj} }
APA Al-solamy, F. R. & Uddin, S. (2019). An inequality for warped product submanifolds of a locally product Riemannian manifold . Hacettepe Journal of Mathematics and Statistics , 48 (2) , 351-358 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/44314/546354
MLA Al-solamy, F. R. , Uddin, S. "An inequality for warped product submanifolds of a locally product Riemannian manifold" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 351-358 <https://dergipark.org.tr/en/pub/hujms/issue/44314/546354>
Chicago Al-solamy, F. R. , Uddin, S. "An inequality for warped product submanifolds of a locally product Riemannian manifold". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 351-358
RIS TY - JOUR T1 - An inequality for warped product submanifolds of a locally product Riemannian manifold AU - Falleh R.Al-solamy, SirajUddin Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 351 EP - 358 VL - 48 IS - 2 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics An inequality for warped product submanifolds of a locally product Riemannian manifold %A Falleh R. Al-solamy , Siraj Uddin %T An inequality for warped product submanifolds of a locally product Riemannian manifold %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 2 %R %U
ISNAD Al-solamy, Falleh R. , Uddin, Siraj . "An inequality for warped product submanifolds of a locally product Riemannian manifold". Hacettepe Journal of Mathematics and Statistics 48 / 2 (April 2019): 351-358 .
AMA Al-solamy F. R. , Uddin S. An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics. 2019; 48(2): 351-358.
Vancouver Al-solamy F. R. , Uddin S. An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics. 2019; 48(2): 351-358.
IEEE F. R. Al-solamy and S. Uddin , "An inequality for warped product submanifolds of a locally product Riemannian manifold", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, pp. 351-358, Apr. 2019