Characterizing Base in Warped Product Submanifolds of Complex Projective Spaces by Differential Equations

Ali H. Alkhaldi; Pişcoran Laurian-Ioan; Izhar Ahmad; Akram Ali

doi:10.3390/math10020244

Characterizing Base in Warped Product Submanifolds of Complex Projective Spaces by Differential Equations

Ali H. Alkhaldi, Pişcoran Laurian-Ioan^*, Izhar Ahmad, Akram Ali

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this study, a link between the squared norm of the second fundamental form and the Laplacian of the warping function for a warped product pointwise semi-slant submanifold Mⁿ in a complex projective space is presented. Some characterizations of the base N_T of Mⁿ are offered as applications. We also look at whether the base N_T is isometric to the Euclidean space R^p or the Euclidean sphere S^p, subject to some constraints on the second fundamental form and warping function.

Original language	English
Article number	244
Journal	Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.3390/math10020244
State	Published - 1 Jan 2022

Bibliographical note

Funding Information:
Funding: The authors would like to express their gratitude to Deanship of Scientific Research at King Khalid University, Saudi Arabia for providing funding research group under the research grant R. G. P.1/135/42.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

Complex projective spaces
Dirichlet energy
Ordinary differential equations
Ricci curvature
Warped products

ASJC Scopus subject areas

Mathematics (all)

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10.3390/math10020244

Cite this

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abstract = "In this study, a link between the squared norm of the second fundamental form and the Laplacian of the warping function for a warped product pointwise semi-slant submanifold Mn in a complex projective space is presented. Some characterizations of the base NT of Mn are offered as applications. We also look at whether the base NT is isometric to the Euclidean space Rp or the Euclidean sphere Sp, subject to some constraints on the second fundamental form and warping function.",

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AU - Laurian-Ioan, Pişcoran

AU - Ahmad, Izhar

AU - Ali, Akram

N1 - Funding Information: Funding: The authors would like to express their gratitude to Deanship of Scientific Research at King Khalid University, Saudi Arabia for providing funding research group under the research grant R. G. P.1/135/42. Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

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N2 - In this study, a link between the squared norm of the second fundamental form and the Laplacian of the warping function for a warped product pointwise semi-slant submanifold Mn in a complex projective space is presented. Some characterizations of the base NT of Mn are offered as applications. We also look at whether the base NT is isometric to the Euclidean space Rp or the Euclidean sphere Sp, subject to some constraints on the second fundamental form and warping function.

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KW - Dirichlet energy

KW - Ordinary differential equations

KW - Ricci curvature

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Characterizing Base in Warped Product Submanifolds of Complex Projective Spaces by Differential Equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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