Geometric inequalities for warped product bi-slant submanifolds with a warping function

In this paper, we prove that the squared norm of the second fundamental form for bi-slant submanifolds with any codimension of nearly trans-Sasakian manifolds is bounded below by the gradient of a warping function and also find the conditions on which the equality holds. Some related examples are al...

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Autores principales: Siddiqui, Aliya Naaz, Shahid, Mohammad Hasan, Lee, Jae Won
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182412/
https://www.ncbi.nlm.nih.gov/pubmed/30363788
http://dx.doi.org/10.1186/s13660-018-1843-3
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author Siddiqui, Aliya Naaz
Shahid, Mohammad Hasan
Lee, Jae Won
author_facet Siddiqui, Aliya Naaz
Shahid, Mohammad Hasan
Lee, Jae Won
author_sort Siddiqui, Aliya Naaz
collection PubMed
description In this paper, we prove that the squared norm of the second fundamental form for bi-slant submanifolds with any codimension of nearly trans-Sasakian manifolds is bounded below by the gradient of a warping function and also find the conditions on which the equality holds. Some related examples are also provided.
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spelling pubmed-61824122018-10-22 Geometric inequalities for warped product bi-slant submanifolds with a warping function Siddiqui, Aliya Naaz Shahid, Mohammad Hasan Lee, Jae Won J Inequal Appl Research In this paper, we prove that the squared norm of the second fundamental form for bi-slant submanifolds with any codimension of nearly trans-Sasakian manifolds is bounded below by the gradient of a warping function and also find the conditions on which the equality holds. Some related examples are also provided. Springer International Publishing 2018-09-27 2018 /pmc/articles/PMC6182412/ /pubmed/30363788 http://dx.doi.org/10.1186/s13660-018-1843-3 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Siddiqui, Aliya Naaz
Shahid, Mohammad Hasan
Lee, Jae Won
Geometric inequalities for warped product bi-slant submanifolds with a warping function
title Geometric inequalities for warped product bi-slant submanifolds with a warping function
title_full Geometric inequalities for warped product bi-slant submanifolds with a warping function
title_fullStr Geometric inequalities for warped product bi-slant submanifolds with a warping function
title_full_unstemmed Geometric inequalities for warped product bi-slant submanifolds with a warping function
title_short Geometric inequalities for warped product bi-slant submanifolds with a warping function
title_sort geometric inequalities for warped product bi-slant submanifolds with a warping function
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182412/
https://www.ncbi.nlm.nih.gov/pubmed/30363788
http://dx.doi.org/10.1186/s13660-018-1843-3
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