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http://hdl.handle.net/10603/363374
Title: | Study of Slant Light like Submanifolds of Indefinite Almost Hermitian Manifolds |
Researcher: | Tejinder Kumar |
Guide(s): | Pankaj Kumar |
Keywords: | Mathematics Physical Sciences |
University: | Maharaja Agrasen University |
Completed Date: | 2021 |
Abstract: | The research work discussed in this thesis is concerned with the geometry newlineof Slant Lightlike Submanifolds of Indefinite Almost Hermitian Manifolds . newlineSemi-Riemannian geometry is the most natural and fruitful generalization newlineof Riemannian geometry. Since the second half of the 20th century, the Riemannian newlineand semi-Riemannian geometries have been active areas of research for geometers newlineand physicists. During the generalization of submanifold theory from Riemannian newlinemanifolds to semi-Riemannian manifolds, the induced metric on the submanifold newlinebecomes degenerate and gives rise to the class of lightlike submanifolds in the semi- newlineRiemannian category. In this case, the study becomes more difficult and strikingly newlinediand#8629;erent from the study of non-degenerate submanifolds as the intersection of normal newlinebundle and tangent bundle is non-empty. For this reason, the results obtained newlinefor non-degenerate submanifolds cannot be applied in the case of lightlike submanifolds. newlineOn the other hand, according to the behaviour of the tangent bundle of a submanifold newlinewith respect to the action of the almost complex structure J of the ambient newlinemanifold, there are two well known classes of submanifolds, namely, the complex newlinesubmanifolds and the totally real submanifolds. In other words, K is a complex newlinesubmanifold of an almost Hermitian manifold, if and only if, for any non-zero vector newlineY tangent to K at any point p 2 K, the angle between JY and the tangent plane newlineTpK is equal to zero, identically. On the other hand, K is a totally real submanifold newlineof an almost Hermitian manifold, if and only if, for any non-zero vector Y tangent newlineto K at any point p 2 K, the angle between JY and the tangent plane TpK is equal newlineto and#8673;/2, identically. Then, Chen [16] introduced a new class of submanifolds of an newlinealmost Hermitian manifold as a generalization of complex and totally real submanifolds, newlinecalled slant submanifolds. newline |
Pagination: | |
URI: | http://hdl.handle.net/10603/363374 |
Appears in Departments: | Maharaja Agrasen School of Basic and Applied Sciences |
Files in This Item:
File | Description | Size | Format | |
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80_recommendation.pdf | Attached File | 2.82 MB | Adobe PDF | View/Open |
certificates.pdf | 162.3 kB | Adobe PDF | View/Open | |
chapter 1.pdf | 434.57 kB | Adobe PDF | View/Open | |
chapter 2.pdf | 405.57 kB | Adobe PDF | View/Open | |
chapter 3.pdf | 398.69 kB | Adobe PDF | View/Open | |
chapter 4.pdf | 335.04 kB | Adobe PDF | View/Open | |
chapter 5.pdf | 395.85 kB | Adobe PDF | View/Open | |
preliminary pages.pdf | 259.4 kB | Adobe PDF | View/Open | |
title.pdf | 496.57 kB | Adobe PDF | View/Open |
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