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

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

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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantic...

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Bibliographic Details
Main Authors: Ali H. Alkhaldi, Pişcoran Laurian-Ioan, Izhar Ahmad, Akram Ali
Format: Article
Language:English
Published: MDPI AG 2022-01-01
Series:Mathematics
Subjects:
warped products
complex projective spaces
Dirichlet energy
Ricci curvature
ordinary differential equations
Online Access:https://www.mdpi.com/2227-7390/10/2/244
Description
Summary: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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>M</mi><mi>n</mi></msup></semantics></math></inline-formula> in a complex projective space is presented. Some characterizations of the base <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>N</mi><mi>T</mi></msub></semantics></math></inline-formula> of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>M</mi><mi>n</mi></msup></semantics></math></inline-formula> are offered as applications. We also look at whether the base <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>N</mi><mi>T</mi></msub></semantics></math></inline-formula> is isometric to the Euclidean space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>p</mi></msup></semantics></math></inline-formula> or the Euclidean sphere <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">S</mi><mi>p</mi></msup></semantics></math></inline-formula>, subject to some constraints on the second fundamental form and warping function.
ISSN:2227-7390

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