Generalized Ricci solitons on contact metric manifolds

In the present paper we prove that, if a N ( k )-contact manifold of dimension ( 2 n + 1 ) satisfies the generalized Ricci soliton equation ( 1.4 ) and X = g r a d f , f being a smooth function, then f is a constant function. Furthermore, if c 2 ≠ 0 , then the manifold is either locally isometric to...

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Bibliographic Details
Published in:Afrika mathematica 2022-06, Vol.33 (2), Article 32
Main Authors: Ghosh, Gopal, De, Uday Chand
Format: Article
Language:English
Subjects:
Applications of Mathematics
History of Mathematical Sciences
Mathematics
Mathematics and Statistics
Mathematics Education
Solitary waves
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Summary:In the present paper we prove that, if a N ( k )-contact manifold of dimension ( 2 n + 1 ) satisfies the generalized Ricci soliton equation ( 1.4 ) and X = g r a d f , f being a smooth function, then f is a constant function. Furthermore, if c 2 ≠ 0 , then the manifold is either locally isometric to the product E n + 1 ( 0 ) × S n ( 4 ) for n > 1 and flat for n = 1 , or the manifold is an Einstein one.
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-021-00944-z