Lorentz Hypersurfaces in Pseudo-Euclidean Space E15

Lorentz hypersurfaces M 1 4 is studied in E 1 5 with non-diagonal shape operators having characteristic equation ( y - λ ) 2 ( y - λ 3 ) ( y - λ 4 ) or ( y - λ ) 3 ( y - λ 4 ) or ( ( y - λ ) 2 + μ 2 ) ( y - λ 3 ) ( y - λ 4 ) . It is proved that if the mean curvature vector field H → of Lorentz hyper...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences, India, Section A, physical sciences India, Section A, physical sciences, 2020, Vol.90 (1), p.123-133
Main Authors: Gupta, Ram Shankar, Kumari, Deepika, Ahmad, Sharfuddin
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Curvature
Eigenvalues
Eigenvectors
Euclidean geometry
Euclidean space
Fields (mathematics)
Hyperspaces
Molecular
Operators
Optical and Plasma Physics
Physics
Physics and Astronomy
Quantum Physics
Research Article
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Summary:Lorentz hypersurfaces M 1 4 is studied in E 1 5 with non-diagonal shape operators having characteristic equation ( y - λ ) 2 ( y - λ 3 ) ( y - λ 4 ) or ( y - λ ) 3 ( y - λ 4 ) or ( ( y - λ ) 2 + μ 2 ) ( y - λ 3 ) ( y - λ 4 ) . It is proved that if the mean curvature vector field H → of Lorentz hypersurfaces M 1 4 in E 1 5 with non-diagonal shape operators satisfies the equation ▵ H → = α H → (for a constant α ), then M 1 4 has constant mean curvature.
ISSN:0369-8203
2250-1762
DOI:10.1007/s40010-018-0542-2