f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms

Shyamal Kumar Hui; Daniel Breaz; Pradip Mandal

doi:10.2478/auom-2019-0036

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f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 27 (2019): Issue 3 (December 2019)

By: Shyamal Kumar Hui, Daniel Breaz and Pradip Mandal

Open Access

|Dec 2019

Abstract

Here we have studied f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms and obtained a necessary and sufficient condition on a submanifold of generalized (k, µ)-space-form to be f-biharmonic and bi-f-harmonic submanifold. We have also studied f-biharmonic hypersurfaces of said ambient space forms.

References

[1] A. Balmuş, S. Montaldo and C. Oniciuc, On the biharmonicity of pseudo-umbilical and PNMC submanifolds in spheres and their type, Arkiv för Matematik, 51 (2003), 197-221.10.1007/s11512-012-0169-5
Search in Google Scholar Back to article
[2] D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Springer-Verlag, 1976.10.1007/BFb0079307
Search in Google Scholar Back to article
[3] D. E. Blair, T. Koufogiorgos and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 19 (1995), 189-214.10.1007/BF02761646
Search in Google Scholar Back to article
[4] E. Boeckx, A full classification of contact metric (k, µ)-spaces, Illinois J. Math., 44 (2000), 212-219.10.1215/ijm/1255984960
Search in Google Scholar Back to article
[5] A. Carriazo, V. M. Molina and M. M. Tripathi, Generalized (k, µ)-space-forms, Mediterranean J. Math., 10 (2013), 475-496.10.1007/s00009-012-0196-2
Search in Google Scholar Back to article
[6] B. Y. Chen, Total mean curvature and submanifolds of finite type, Ser. Pure. Math. World Scientific Publishing Co., 1984.10.1142/0065
Search in Google Scholar Back to article
[7] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, American J. Math., 86(1) (1964), 109-160.10.2307/2373037
Search in Google Scholar Back to article
[8] J. Inoguchi, Submanifolds with harmonic mean curvature vector field in contact 3-manifolds, Colloq. Math., 100 (2004), 163-179.10.4064/cm100-2-2
Search in Google Scholar Back to article
[9] J. H. Jiang, 2-harmonic maps and their first and second variational formulas, Chin. Ann. Math. Ser. A, 7(4) (1986), 389-402.
Search in Google Scholar Back to article
[10] W-J. Lu, On f-Biharmonic maps between Riemannian manifolds, arXiv:1305.5478, (2013).
Search in Google Scholar Back to article
[11] Y-L. Ou, f-harmonic morphisms between Riemannian manifolds, Chin. Ann. Math. Ser. B, 35 (2) (2014), 225–236.10.1007/s11401-014-0825-0
Search in Google Scholar Back to article
[12] Y-L. Ou, On f-biharmonic maps and f-biharmonic submanifolds, Pacific J. Math., 271 (2) (2014), 461–477.10.2140/pjm.2014.271.461
Search in Google Scholar Back to article
[13] S. Ouakkas, R. Nasri and M. Djaa, On the f-harmonic and f-biharmonic maps, JP J. Geom. Topol. 10 (1) (2010), 11–27.
Search in Google Scholar Back to article
[14] D. G. Prakasha, S. K. Hui and K. Mirji, On 3-dimensional contact metric generalized (k, µ)-space-forms, Int. J. Math. and Math. Sciences, Vol. 2014, Article ID 797162, 6 pages.10.1155/2014/797162
Search in Google Scholar Back to article
[15] J. Roth, A note on biharmonic submanifolds of product spaces, J. of Geometry, 104 (2013), 375-381.10.1007/s00022-013-0168-0
Search in Google Scholar Back to article
[16] J. Roth and A. Upadhyay, Bihrmonic submanifolds of generalized space forms, Differential Geometry and its Applications, 50 (2017), 88-104.10.1016/j.difgeo.2016.11.003
Search in Google Scholar Back to article
[17] J. Roth and A. Upadhyay, f-biharmonic and bi-f-harmonic submanifolds of generalized space forms, arXiv. 1609.08599, (2016).
Search in Google Scholar Back to article
[18] M. M. Tripathi, Certain basic inequalities for submanifolds in (k, µ)-spaces, In: Recent advances in Riemannian and Lorentzian geometries (Baltimore, MD,), Contemp. Math., 337 (2003), 187-202.10.1090/conm/337/06061
Search in Google Scholar Back to article
[19] K. Yano and M. Kon, Structures on manifolds, World Sci. Publ. Co., Singapore, 1984.10.1142/0067
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2019-0036 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 97 - 112

Submitted on: Sep 26, 2018

Accepted on: Oct 8, 2019

Published on: Dec 21, 2019

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

generalized (k,µ)-space-forms,

f-biharmonic submanifold,

bi-f-biharmonic submanifold,

f-biharmonic hypersurface

Related subjects:

Mathematics,

General mathematics

© 2019 Shyamal Kumar Hui, Daniel Breaz, Pradip Mandal, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 27 (2019): Issue 3 (December 2019)